.Larger bore sizes work better in shorter barrels,but they suffer from a BC disadvantage due to the fatter bullets.
Which is what makes 7mm-08 & .308 (and even .30-06) very well balanced rounds for shorter barrels, still having respectable BCs with lighter bullets they can drive at decent velocities.
That said, if ranges are more moderate, .338, .358 and .375 caliber cartridges are a great choice. .35 Rem does very well from short barrels, and with a more sedate bark for the unsuppressed crowd if you need a <200 yard deer round. Stepping up, you have the .358 Win, .35 Whelen and .350 Rem Mag, which also don't need really long tubes. .350 rem mag has a similar same bore area to powder charge ratio to .308 Win, .35 Whelen is slightly lower.
To do the math, just divide powder charge by bore area in inches. The higher the number, the more velocity will suffer in short barrels
.243 Win 45 gr charge = 962
.25-06 55 gr charge = 1,062
7mm-08 46 gr charge = 726
.308 Win, 46 gr. powder charge= 617
.30-06 52 gr charge = 698
.300 Win Mag 70 gr charge = 966
.300 Rem ultra mag 100 gr charge = 1,342
.35 Whelen 57 gr charge = 566
.350 Rem Mag 60 gr. charge = 594
For reference, the highly efficient .22 LR and .45 ACP score about 44