I would think a 308 or a 7mm-08 would both work quite well. Not a ton of data on the 7mm08, but seen some load reports at respectable velocities down to 18.5" and woukd bet it would do pretty well down to 16. Lots of data showing 18" working well on the 308.

The smaller projectile loads, 260, 6.5CM, 243, 6CM all like just a bit longer barrel before really shining. I'd take the 243 from that lot in a short bbl if I had to choose.