Remington's got their 16" 700 chambered in .300 Blackout - basically a modernized .32-20.
One could load something like the plain based, hollow point versions of some NOE's .30 carbine bullets atop a light charge of fast pistol powder. That would get you in the 110 grain (ish) range. With some tinkering, you could probably seat a 00 buck pellet atop the round.
Plus the round gives you the ability to go up to 220 grains or so. . .for when that squirrel with the M249 shows up.