Best thing to do: go look at a load manual or two, and see what you see.
I regularly load .308 Win with 155 bullets, using medium speed rifle powders (4895, Varget, Rel-15, N140, etc). I occasionally load .338 Win Mag with 250 or 300 grain bullets, using slow rifle powders (e.g. 4831).
I would look to see if there a reasonable loading for .338 Win and 225 grain bullets using a medium speed rifle powder
I just looked at
http://data.hodgdon.com/cartridge_load.asp and here's what I see;
- with full case of the slow rifle powders (4831, 7828, etc), you can get about 2800fps
- with powders which would be good for a .308/159 (H380, Varget, 4320, 4064, 4895) you can get 2642-2764fps using about 10-15 grains less powder than one of the slow powders.
I would expect that if ~2700fps max speed was OK with you, one of the loadings of (H380, Varget, 4320, 4064, 4895) ought to work well for you.