Gunman,
Most ecomonical conversion would be something like a 284 Win. I know its an old round but I assure you that with modern bullets it is a very potent long range option for a short action rifle.
TO be honest, I would recommend loading the rifle as a single shot anyway so you can set heavy long bullets out farther so they will not take up so much case capacity.
Again, if you take a 284 Win loaded with one of the upper BC 175 gr bullets or even a 162 gr A-Max or 160 gr accubond for hunting.
A bit more extensive conversions, again, single shot options here, the WSMs are a good choice. anything from 6.5mm to 30 cal in the WSM case would be a significant step up in ballistic horsepower.
Of these, I would look at the 6.5 or 7mm first. With the use of a Wildcat ULD RBBT in 169.5 gr weight the 270 version would be equal to most 7mm WSM loads or even surpass many ballistically.
The 30 cal is fine but you need alot of bullet weight to match the ballistic performance of the smaller caliber rounds. Barrel life is increased with the 30 cal but ballistic performance goes down slightly and recoil increases significantly.
For a short action, thats about it in my opinion.
If you are just punching paper or varmint hunting, I would also agree a 6mm BR, 6mm-250 or 243, 243 AI or 6-284 with a proper twist barrel with heavy match bullets will also work very well at long range. For deer size game they are a bit light but for everything under this size game they will work fine.
Good Shooting!!
Kirby Allen(50)