So, do you have pictures of the 37?

The last 39 Plymouth I had, I did the disc brake conversion and the Caviler rack & pinion. I didn't get around to doing the upper shock relocate before someone needed the car much more then I did (I had to put a motor in my work truck at that time). I also did a 39 with a Dakota front clip, but I didn't get that one done either, before it went down the road (I'm seeing a growing pattern here. )
I have, however completed a Dakota swap on a 48 Plymouth, and my current car has the full Dakota frame under it.

The wheels on a Dakota (87-90 are 5 bolt wheels, 91-96 can have the 6 bolt wheels changed to 5 bolt by just swapping the 5 bolt parts, swapping to 5 bolt wheels on the 97 & newer is not an easy task) are factory inset by about 2" compared to the old style wheels, and I believe the Dakota has a 60" track. That puts the stock offset Dakota wheels close to the fender edge. If you intend on slamming it to the ground, I suspect the tires will rub the fenders, or be very close. At normal ride height, everything should be OK.
With the Dakota, just like any time you change the frame, you will need to fabricate a radiator support for your 39.

Between the Dakota and the upgraded original frame, if your original frame and suspension is in good condition, its tough to beat the original frame, and I suspect the final cost is going to be about the same money spent. To do it right, any way you go, should have new brakes, rebuilt suspension, new shocks, and rebuilt steering box/rack.

I've not ever done a Mustang II front end, and the money spent is about the same. Gene