Drawing or sizing the bullets down is the proper terminology, Bob. I found that out the same way.
Lee makes lead (& usable with jacketed) bullet sizing dies &, for about $30.00 each, will make you dies for sizing down the bullets to whatever size you need. This custom work was not mentioned on thier site last time I looked.
The best result with their dies is .003" per die, so to go down to .354",you'd need 2 dies - maybe. Since it's only .004", a single die might be all that's needed and there could be .0005" spring-back on that .004" reduction. The spring-back makes picking sizes a bit important, but know, a thou here or there is not important, as long as the rounds chamber easily and the bullets will slide into a fireformed case easily. If not, the necks are too tight or bullets too large for that rifle.

Lee has been doing this for a few nears now and has developed some experience making them for jacketed bullets thanks to Rod Halverson's (Idaho) insistance and experimentation. A local friend of mine reduces 220gr. 8mm's to .314" for his .303 and 200gr. .338's down to .330" for his 8x56R, both using a set of 3 Lee bullet sizing dies.

The DS rifle might need 2 dies to get down to .352" or .3515".

As to trading off my 9.3x57 - I'll be getting another - maybe a M146 this time so I can make around 2,275fps to 2,325fps with 286's. It's too great a round not to have one. I still have my 9.3x62 Oberndort and the .375/06IMP. The opportunity to get my M94.356 back from my brother could not be missed.