Not quite on the '06 performance in a 20" barrel. My father has one of the savage stryker pistols with a 14" barrel in 300 wsm
and it will turn in average '06 sporter velocities.
If you want to do this you will loose some speed, and you will land midway between the '06 and 300 win in actual velocity. I've been working with contenders and strykers for years, and 400 fps loss to go the pistol barrel is about it.
The trick is to find a powder whose energy is expended by the time it gets to 20". Use the fastest powders that produce full velocity in your cartridge. rl17, 4350(both h and imr), 760, etc. for mid weight bullets in the 300win. If you step up to 180, I'd go to 4831 class, but no slower than rl22.
If I were a betting man, I'd say you can still net 3200 fps with a 150 and 2900 fps with a 180.
P.S., the short barrel absolutely helps accuracy. My stryker pistol (22-250) will pitch 5 shots into an inch at 100 yards with one sandbag under the heel on the pistol(4x leopold on top), and I've killed prarie dogs at 1/4 mile with one of my father's strykers.