You might be able to port the barrel enough somewhere between full power and subsonic using a fast pistol powder so the pressure builds fast then drops fast. Like I said it will be an uphill pull and obviously far easier on an ar platform.
You have to ask yourself is getting 60 grain heavier bullet 30 cal 240 SMK .685~ bc vs 338 300 SMK .750~ bc and a little better bc worth all this extra effort.
Another option to get the power you are looking for in the 338 cartridge would be to run the powdered tungsten bullets This company makes the best powdered Tungsten bullets out there.
http://www.drtammo.com/products.html
DRT makes a 124 grain 223 bullet you might try to get some of those and run it through your 93 and see if it would cycle subsonic with that heavy a bullet. Or you might buy some powdered tungsten 308 bullets they make a 280gr PT bullet that is the same footprint as a 208 amax awesome bullets but very expensive like 3-4 bucks apiece but compared to buying a custom barrel or having custom locking pieces built then finding out it wont' work after all and you have a very expensive straight pull bolt action.
You might try to take a 91 and run subsonic 308s through it and see if you can get it to cycle with a lighter mainspring and different locking piece before you start spending a lot of money on a custom barrel.
Just some ideas and Options
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