Dear Bear,
I can see why you are interested in the .375JDJ. You would be able to load to your required energy level with considerably less pressure than the .375 Winchester requires to get that result. I looked at the dimensions of the two cartridges, and while the rim of the JDJ case (12,95mm) is only slightly wider than the old Winchester case (12,85mm), it is nearly 15 mm longer. I think this may cause real problems with the magazine and receiver feed mechanism. You can use a wood dowel that just slips inside a .375 Winchester case, but cut it to stick out to 80 mm. Whittle a narrow spot in the dowel just ahead of the case so it is easy to break off if it gets stuck in the gun. Now you can load this dummy round into the magazine and see if it still can be chambered without hanging up?
The only possible solution I could see in the same case length is to make a wildcat by necking a .430JDJ to .375. The .460JDJ case rim (13,06mm) is also a little wider than the other two cartridges, but there is still a chance it may fit your gun. You would have to try a case or else take a bolt face diameter measurement to predict it.
Before you consider either conversion, you want to acquire actual cases or turn them from wood to see if the magazine and feed mechanism will accomodate them?
Nick