Hmm, the 300 yards definitely adds another dimension to your thought provoking project.
I have just never considered the higher intensity bores smaller than .375 for 20" candidates. I am certainly not saying anything wrong with it.
The 350 Remington certainly seems to do well with the 20" barrel. If I recall correctly the 338 RCM also does well. It would be interesting to see how the 325 WSM would do with 20". Though, I am not curious enough to go below 22" with mine. I would guess 2600-2650 fps would still be feasible with a 200 grain bullet. Possibly even 2700 fps or more. That would give roughly an allowance of 200 fps loss for 4" less barrel than the 24".
Not applicable to your build but, I am in the process of having an approximate 19.5" 35 Whelen put together. Maximum intended use is 230 yds. Which is about three times the distance of visibility where I intend to carry this rifle.