This is only a wild guess, but have you considered that the other side may not be applying as it should, something out of place in the assembly, and the locking side is trying to do all the work, and the front is working normally?

Just a shot in the dark ... years ago had something similar, but on the front, that turned out to be a collapsed rubber hose, internally, stopping the flow to one wheel, and making the other do all the work.

Have you tried tightening the adjustment on the problem wheel? Too loose can allow the shoes to overtravel and jam against the drum rather then apply smoothly.

Are the drums the correct diameter? An oversized drum has the same effect as loose adjustment.

You will have eliminated a lot of questions by doing so and can then move onto the assemblies themselves

Another thought crossed my mind, actually 3:
1. Are you 100 % sure the brake cables between the backing plates and main cable are free and not sticky
2. Possibly try swapping springs side to side. A long shot, but if the one side has weaker springs it will apply sooner.
3. One could try a thin layer of contact cement and thin sandpaper on the inside of the drum. Spay a very light coat of lacquer paint or machinists dye on the shoes, install the drum and see if there is a pattern difference side to side.

I believe you said you swapped the shoes so that would eliminate the friction compound.
Keep us posted

With the shoes off, run your finger across each pad. If you can feel anything except a smooth flat surface, it could be your problem. Sometimes it really doesn't take much surface difference at all to cause a problem, but I have also had the pads feel and look like they have Grand Cannon grooves that don't seem to make much difference.

Does the car have self adjusting brakes? We had a customer once that lived on a one way street, they backed out of their driveway in the same direction every time they went someplace. The self adjuster on one side would tighten the brakes more then the other side, and the first few stops would cause one wheel to lock up. After a few brake applications, it was good until the next time they left home. It just happened the boss was driving by one day when they backed out of their driveway. We removed the self adjusting cable for a week, and the problem went away. After we reinstalled the adjusting cable, the problem came back. I think the boss suggested they change how they back out of the driveway. Anyway, just another possibility, since your looking for strange stuff. Gene

Are the wheel cylinders the same on the rear, left and right? If so try switching wheel cylinders. If you still have the problem at the same wheel (left rear I think you said) then back the shoe adjustment off and see if you can get the right side to lock with it adjusted correctly? If not the you would have a line restriction from the single flex line distribution block on the axle housing.

I’ll try and answer all questions.

All rubber hoses (two up front, one in the rear) were replaced with new.

I did tighten the adjuster on the problem wheel, then I loosened it significantly and about 20 different spots in between. No joy.

The drums are correct for the vehicle and all are matching. I’ve also switched drums around and the same wheel locks up.

The e-brake assembly was loose but I will have to completely disconnect and remove the e-brake lever from inside the drum to rule it 100% out.

I did swap brake shoe return springs from side to side, didn’t work.

The shoes seem to be wearing smooth and there are no self-adjusters on this car.

Wheel cylinders are different for each corner of the car.

Try bleeding each wheel cylinder especially opposite the problem corner by removing one drum, pumping the brake pedal until the wheel cylinder pistons are out as far as possible (without falling out of course) then have someone hold the brake pedal down on the last pump, open the wheel cylinder bleeder, push the wheel cylinder pistons back in to purge any air out of the entire wheel cylinder. You might only need to do that with the wheel cylinder opposite the locking brake drum,........hopefully.

Starting to seem to me that the locking drum is actually free of air in the line and taking all of the master cylinder pressure and working correctly. While the other side still has some air in the system and just spongy??? Just throwing stuff out there to see what sticks.......besides the one brake drum Sorry not funny, apologize good luck

Mike

There is the old, tried and true method....vice grip one brake line shut. LOL. Sorry..that was the old 'fix' when we had a bad wheel cylinder back when I was in high-school.

Trust me, that has crossed my mind!!!

OK....so I'm not the only one that got creative in their youth when money was tight!

I had a similar issue on my 49 International truck. I'd hit the brakes, and the truck would turn left. I tried adjusting the brakes to no effect. As these brakes were old drums, and many of the parts were unobtanium, I put a disc brake kit in. Couldn't get the front to bleed. Finally out of frustration I pumped the crap out of the brake pedal. Found a tiny rust hole in the hard line. Not enough to show a leak normally, but enough to not allow the right brake to apply. Something to look for...

This is going to be difficult to explain, but this has cured a similar issue for me. On the top and bottom of the shoe material where the material meets the shoe itself on the upper and lower edges is it 90 degrees or beveled? I had to bevel some shoes before because they were really grabby. I smoothed the radius out because that sharp edge would grab and cock the shoes. Be careful as they may be asbestos.

But the bore on the fronts are the same and the bore on the rears are the same? You don't have wheel cylinders with different bore sizes on the same axle?

If you do not want to do the above

Did you move the drums with the shoes ???

One could also move the backing plates side to side ( except for the ebrake cables being hooked up)
.
You appear to have done everything but the pressure test and the backing plate swap. So I might just consider swapping the entire assemblies side to side.

A long shot but make sure the RE bushings , spring mounts U bolts etc. are all in good consition. I had one several years back that had a brake pull to the right. It had been to several shops and the customer wanted disc brakes. When the car came in the front cross-member was rotted 3/4 of the way around on the right side. I had him drive 60 miles to see it for himself. It was baltantly obvious yet 4 or 5 shops did not see it. You might need someone else to take a look at it.

"Just touching the brake pedal at 20 mph locks up the wheel." I call that grabbing more so than locking. When that happens, it's almost always the self energizing characteristic of drum brakes malfunctioning. One way to know is if it only happens going forward. If it doesn't grab in reverse, it is the a self energizing malfunction. If the anchor pin is mispositioned rearward, or especially if it is low due to a bent backing plate, or a junk chinese repop backing plate, it will cause grabbing. Or if the anchor pin is worn, allowing the top of the front shoe to retract too much. I would try a different backing plate and/or anchor pin. Also, grinding the top of the lining of the front shoe to a bevel could help, but it is a crutch, not fixing the cause. Good luck, Joel

Brake systems of that era can be different than later stuff, I daily drive a 51 Plymouth so I understand.

I also understand the hacks prior owners can inflict on old cars. You say the brakes have always bee iffy and the one wheel has always locked up.

You say that you've pretty much replaced everything, except hard lines.

I know nothing about the braking system on a 57 Chevy so I started googling. Lots of disc brake swap kits came up, damn near zero "how to rebuild the stock rear drum" info though.

The problem I see is how do you know it's put together correctly? If you put it together the way it came apart you may have just reinstalled the problem only with new parts.

Here's a shot of the rear brakes from trifive.com for reference. Key thing to remember that the parts are installed in reference to the front of the car, not your left or right. For example, the ebrake lever will be on the rear of the assembly which means on one side it will be on your right, but on the other it'll be on your left. All parts will be like that. Sorry to be so basic but that will sometimes bite even the best of us.

Exactly. The front wheel cylinders are larger bores than the rears but each axle has identical size bores.

Good ideas. I have not moved the backing plate or drum w/shoes to another wheel. I'll try that, and the pressure test.

I have checked the spring mounts, etc, decent shape. I have had a couple of friends to bebuild cars look at it and they are stumped too.

Great idea, I've never tried it in reverse. I'll go out and do that.

I believe the shoes were beveled from the factory but I'll have to check and make sure.

Not a problem!!!! Right now I need to get back to basics!! I'll check my work.