Cold, my car was the same way. Almost impossible to push.
But after i make a pass i can push it easily.
I think its the tight clutch pack in transmission??.

My son had an issue with his line lock that was causing his front factory disk brakes to drag. He disconnected it two years ago and all is well

Too much camber or toe

I noticed my car was harder to push backwards than it had been, at the same time had a small differential leak. I took the driveshaft out and found the pinion nut just hand tight. I put a new nut on, with loctite, around 250 ftlbs, and it was then back to normal in terms of how hard it is to push, and no more leak. I also engraved the pinion and nut so that I can look in and see that the nut is where it was when torqued in.

Not a race car, but my 67 GTX convert is hard to push. 727 trans, 8-3/4, drum brakes, 50,000 original miles. I made sure the brakes are not dragging. I think it's something in the trans. I'll be watching here.

The car will be harder to push rearward due to more internal components rotating in the trans when the output is turned counter clockwise. Even though my trans is mostly roller bearing, it is still very tough to push. Yet on the hoist you can rotate the drive shaft with one hand (spool, axles. brakes, wheels/tires installed).
Doug

If you have a spool that's the reason for it being hard to push even for 3 people, prior to the spool i could push the car by myself.

Sounds like your rear tires are not the same diameter based on pushing harder now with the spool compared to before
I used a cloth seamstress tape to measure the circumference of all my tires regardless if going on a spool rear end or not

Did you ever figure out the problem ?

My car was always hard to push and it turned out that the pinion nut was too tight and the crush sleeve was crushed too much.

Does the Master cylinder have a residual valve for drum brakes in it? If so it will hold close to 10 Lb. pressure on them