I will keep this simple, TO MUCH CASE!!!
A 100 gr bullet would help alot if it could handle this velocity level. In my testing, the 100 and 107 gr ULD RBBTs needed a 1-7 twist to stabilize, only problem, in this twist rate, your limited to around 3100-3200 fps max before they come apart.
The 06 case is just more then needed. In fact, a 22-250 AI will get you this velocity level with these bullet weights.
For lighter bullets, its just to much case capacity to be practical. For bullets from 55 to 80 grains, something like a 22-6mm will do anything the 06 case will do easily!!!
I played with a similar capacity 22 wildcat when developing my 224 Allen Magnum. I will admit it was not a successful project. If we had a 100 gr bullet that would take the velocity it would be a totally different story but we do not have any that would work really well at a practical price.
If it were me, I would not go any larger then a 22-6mm AI capacity chambering. Even the 22-284 is just to large in my opinion for the bullets we have right now.
Hope this helps. To be blunt, spend your money on another project, this one will be very frustrating. Now if you bump up to 6mm, totally different story!!! Amazing what 19 thou in bullet diameter gets us for stouter bullets that will take the speed.