After some minor work to my forend (turns out all that was needed was "floating" the forend on the stud with a washer), my Handi is more accurate than I am, even after having not cleaned it in like 150 rounds, and during a "rapid fire" string of like 30 shots in about 6 or 7 minutes.
I cut my .308 barrel to about 16.5" (16.4" after filing) and, while it is still more accurate than I am, I wouldn't use it for hunting much past 200 yards unless I got a lot of practice at range estimation between 200 and 300 yards. Part of it is the moderately-reduced velocities (around 2600-2650fps rather than 2850-2900fps from a 24" barrel, using the same loads), but part of it is because I now stick to moderate starting loads. I do the latter to both reduce muzzle blast because the short barrel only exacerbates it, and to increase case life and slightly reduce recoil.
But, I can push a 150gr bullet to about 2500fps using a very moderate load (about 40k PSI-- using a bit below the starting powder charge). With a 190yd zero, I get 2.1" of midrange rise and it drops to 2.5" by 225 yards and on to 5" by 250 yards. So, it has a PBR of about 225 yards assuming a 5" hit zone. Now, it has the velocity to be effective to well beyond 300 yards with a quality hunting bullet, but it would just be hard to get a reliable hit. So far, everything but a ~Max load of my current powder (H335), including two types of factor ammo, have had about the same level of accuracy.