The Winchester 100 semi-auto hunting rifle from the late '50s to early '60s came in a number of short action calibers including .284. I had one in .308. A buddy had one in .284. They are very rare and collectable now.
Anyway, the .284 had to use special magazines just for it with different feed lips because of the very issues you are identifying. Maybe careful study of the design of the feed lips from photos of those Win 100 detachable .284 magazines would give you some clues on how to modify your mags to make them work.
The .284 was a great round and has proven its worth by subsequent wildcat modification to the 6.5-284 and other variants.
Here is a photo of an original Model 100 .284 magazine. Notice how wide and how far back the lips are. I also note from your photo that you are probably going to have to seat the bullets quite a bit deeper, forcing use of lighter bullets or give up quite a bit of case powder capacity.
FWIW, that's why many of us that wanted higher velocity flatter shooting 7mm center fire rifles from that era (I'm 65), went with the long action .280 Remington, where we did not have to worry about magazine length or having to compromise on bullet weight or shape. I'm still a .280 fan. Sorry for the diversion. I hope the photo helps. I admire your persistence. A 7-08 would certainly be a lot easier.