Take your .357 bullet and let's say you can push it to 1350 FPS at the muzzle and let's use this bullet for example 205gr with an estimated BC of .24. That gives you 825 FPE at the muzzle, which would be just HUGE HUGE power from a .357 AG. The Texan is listed at 300 FPE with a 190gr as a reference. But let's say you get there with your BHAG (Big Hairy Audacious Goal)
You are starting out at Mach 1.21 AWESOME!!! , but at 125-135 yards your bullets has slowed to Mach 1....Bad news from there. Between 135 and 160 yards your bullet has dropped below Mach 1 and is now hitting that nasty transonic speed zone that will destabilize the bullet and there goes accuracy out the window.
But let's dial it back a bit. You said 40% more power than commercially available AG's. Again let's use the Texan in .357. at 300 FPE That would make your BHAG 420 FPE.
Now that same bullet at that energy would have a muzzle velocity of 962 FPS, which is good because it keeps the bullet out of that nasty transonic zone...right?
The bullet will then have 129 inch of drop at 300 yards and 9 inches of wind drift (with a 5 mph 90 degree wind) and it is dropping like a rock at this range. Miss your yardage by 10 yards and the POI changes by 12 inches.
Not raining on your parade, but pointing out the realistic physics of an AG
The balance has to be found between Speed, Bullet Weight, and BC.
Again Chairgun software (It's Free) is a great tool for running what if cases in your design. This is not like powder cartridges where there is a load data book and published data for cartridges at different loads. It is more like building wildcat loads, just no brass or powder....lol
https://www.hawkeoptics.com/chairgun-and-x-act-end-of-life.html