I expect all speeds are calculated. But it can be done. Shooting over a chrony would be a risky proposition. But building a ballistic pendulum to catch the bullet and lock at its maximum point of swing should be doable.
I can think of one way to make a 300gr bullet stable at 1:8 twist. Not guaranteed mind you. And it won't shoot from an AR because of seating depth unless you single load. Even then I wouldn't recommend it.
Make a full wad cutter hollow point. Make it hollow all the way down to the base with just enough in the base for the charge not to blow through. By pushing the mass to the outside, you will get a more stable bullet.
The 240 SMKs already tend to pass through game from what I've heard. Major penetration. So if you want more mass on target, you might want to look at the 458 SOCOM.
Having spent a happy Sunday afternoon launching 240 SMKs around the place at different velocities I would say that the down range energy transfer is impressive. I vote to not stand in front of one on the off-chance it goes straight through.
Powell river laboratories did make a some 280 grain powdered tungsten bullets for some government contracts but at $4 a piece that gets pretty pricey. Not all of us have the governments budget. DRT purchased the right to use Powell river labs tungsten bullets and make current loaded ammo but none that heavy. Most are around 200 grains.
Ah, but we do - the "government's" budget is looted from our wealth, it has none of it's own......
If you have the means to lathe turn your own bullets, you could do a fin stablized projo - I have a brass .50 BMG fin stabilized bullet I designed and made somewhere in my desk drawer.
Nice use of driving bands there. Should keep pressure levels safe and lengthen the life of the barrel.
I've seen artillery shells that only use one or two driving bands. Would that still work and save you some machining? Or are you trying to keep every last grain of material you can?