Man I'd get it. I had one in .223Remington that I bought brand new in 1979. It would shoot 3 55 grain FMJs into 1/2 inch. With a .22-250 it may set the bolt head back but If you get a new barrel I think it would take quite a few rounds to cause a real problem. Just FL resize if you hand load and watch your cases for signs of stretching that could cause Incipiate Case Head Separation, which can be dangerous. Get a 26 inch barrel and later if it shows to have developed excessive head space just have it set back. That's the case for a 26 inch barrel, you got more to use. Just don't hot rod it too bad. A .22-250 is fast enough aleady. Also, I wouldn't try to use it on something like prairie dogs where you shoot a large volume at each session. A .223 would be a better choice for high volume because it's much easier on barrel throats.You could conceivably burn out the throat in as few as 8 to 10 prairie dog hunts with a .22-250. I use mine for deer, turkey, coyote, and yes ev en hogs and whatever else I need it for. Many a deer around here has fallen to a .22-250 with a 55 grain bullet and a head or neck shot. They do have their following in deer camps in Texas.
But I do have a soft spot (and I don't mean on my head) for a 788. They are accurate beyond all expectations. And you already have a nice stock and a Timney Trigger so in my humble opinion it would be worth it.