I would use IMR3031 as a traditional standard for 303 British, 450/400, 450NE, 450#2, 465NE, 475#2, 470NE, and 500NE.
I would use IMR4350 as a traditional standard for 7x57R, 375 Flanged, and 375HH.
You *can* use IMR3031 for everything, but with the 7x57 using heavy bullets, and generically for the 375s, 4350 is a go-to, highly accurate, very standard powder.
Correct. I know you can rush to the online gun shop and buy ten lifetimes of Hornady DGX/DGS today for virtually all of the calibers you're interested in. IF on backorder, you'll have them within a year for the odd one you cannot find. Its the easiest path to ample supplies.
For 7x57r and similar, I would select just a soft point, one you really like, and I'd buy a trove of them. No solids required.