Here are my picks for top Handi-Rifle long distance performers-assuming a 100 yards zero on all. I'll go to 600 yards because not many Handis will really be competitive past there. Bring on the verbal abuse

I think any of these could drop the hammer on a deer at 600 yards if placed well.
243 with 95 grain SMK's at 3100 fps. (I use a .5 BC for these out of my 6mm Ackley at 3400)
If it had a faster twist it could really show some surprising ballistics.
300 yards
3.2 moa drop, 2541 fps & 1361 ft lbs
600 yards
10.8 moa drop, 2047 fps, 883 ft lbs
7mm-08 with 168 grain Bergers at 2700 fps
300 yards
4.3 moa drop, 2280 fps, 1938 ft lbs
600 yards
13.8 moa drop, 1899 fps, 1345 ft lbs
280 Ackley with 180 grain Bergers at 2850 fps (my favorite)
300 yards
3.73 moa drop, 2315 fps, 2140 ft lbs
600 yards
11.9 moa drop, 2070 fps, 1712 ft lbs
308 Winchester with 208 grain Hornadys at 2600 fps
300 yards
4.73 moa drop, 2208 fps, 2248 ft lbs
600 yards
14.83 moa drop, 1852 fps, 1582 ft lbs
30-06 Ackley with 208 grain Hornadys at 2850 fps (SHOCKING ballistics!)
300 yards
3.8 moa drop, 2436 fps, 2739 ft lbs
600 yards
12 moa drop, 2058 fps, 1955 ft lbs
So there ya have it, my top picks. The 280 Ackley with 180 Bergers is capable of some sweet ballistics at relatively low recoil, however if you're after max power the 30-06 Ackley can absolutely whoop up on factory 300 Win Mag loads! A friend has a 30-06 Ackley with a 22" barrel and gets 3k fps from 200 grain Accubonds. I slowed it considerably for comparison here, as that is one hot load.