From my experience with developing the .366 DGW I would guess you will be about 300 feet per second behind the .378. The .366 DGW is based on the .416 Rigby case and thus has a lot more case capasity then the Ultra case. I can push 250 grain bullets at 3253 FPS with 54,800 C.U.P and 300 grain slugs at a bit over 2900 with 48,000 C.U.P. Your Ultra running simular pressures should be 150 to 200 fps slower.
As to loading data I would start with the middle loads for the .338 Ultra, since your bore size is larger you can push your bullets the same speed with less pressure. Check for pressure as you work up from there. You should find that IMR 4350 will work well with the 250 grain bullets and either H4831 or the IMR 4831 with the heavier bullets. Do not try the 320 grain bullets as they are designed for only 1800 to 2200 fps and you will find the true meaning of bullet failure with them. Also if you want to run the 286 grain Barnes X bullet you will need a 1 in 12 twist or keep the velosity around 2800 or the do not stabilise. (They are about 1/4" longer then a 300 grain Swift A Frame). Good luck, have fun, be careful, and I hope I have been of some help. If you have any questions feel free to call me our shop has 20 years experience in working with Wildcats.