I put a 48 Plymouth coupe on a 90 Dakota frame and it worked out really well (100K miles now). I believe the 48 is a couple inches wider then the early 30s cars.
I also had a 39 Plymouth coupe with a Dakota frame, that one also cleared but were pretty close using the standard offset Mopar 7" wide steel front wheels, but I believe it too is wider then the early 30s cars.
I believe the fenders got wider on the front by 35 or 36. The 35 I built had am F,M,J clip (before the Dakota existed), but I needed to add 2" on each side for the tires to clear (they did clear easily). I believe the F,M.&J clip is wider then the Dakota, and that car used the standard off set 7" aluminum slots.
I believe the Dakota frame is going to set the tires real close to the edge of the front fenders on that 33 Plymouth coupe, even if you use the inset Dakota wheels. If you don't mind moving the front fenders out an inch or so on both sides, and don't drop the front end to the ground, it will work OK.
A picture with a good view of the 48 Plymouth tire in the front fender.
The only picture I have of the 39 is a side view with the tires turned a bit, so that won't help you much, but I'll post it anyway.
The picture of my 35 doesn't really help because everything is different.
A stock early Dakota 6" wheel has the center moves towards the outside about a full inch more then a standard factory 6" wheel, which moves the tire inward the same distance as the wheel center moved (if the wheel center moves out 1", the tire moves in 1").
