I use pulled down 7.62x39 bullets in .303 all the time. Probably one of the most economical ways to get .311 bullets.
The how is easy: A kinetic puller works. Surplus rounds tend to take a couple whacks, but it works. Pulled bullets from surplus 7.62x39 and 7.62x54R are .311 diameter and are good to go for .303. My Enfield slugged .313 but shoots .311 jacketed just fine.
Reusing the powder charges is an interesting game. From 7.62x39 rounds, you can dump the whole powder charge into a .303 and it'll make a nice moderate load that isn't as punchy as factory .303. It keeps things economical for sure. If you want to make things a bit more precise, dump all the powder charges into a container, then give each .303 a uniform charge. This will eliminate the factory tolerance (variance) in powder charges.
7.62x54R on the other hand is rated for higher chamber pressures than .303 - on the order 3000-6000PSI more. Thus, using the entire powder charge in a .303 is a recipe for a KB. Downgrade the charge and slowly work your way up if you want to reuse that powder.
If you'd rather use commercial powder, Hodgdon has load data for .303 for 125Gr, 150Gr, 174Gr, and 180Gr bullets, which should cover off most surplus. YMMV with usual caveats: .30-40 Krag is a very comparable cartridge - look at its load data if you need more powder selection, particularly with pulled 7.62x39 bullets (look at 130Gr data). If you want a milder load, 7.62x39 load data might be a good starting point: I've successfully used 22.2Gr IMR 4198 behind a 123Gr pulled bullet. Again, YMMV with the usual caveats.