Quick and Mitchell.
It seams that many people believe that poor accuracy comes from a poor barrel. Of course a poor barrel will not shoot as good as a good barrel.
I have seen 303 barrels that were so bad but still shot with 1-1/2 accuracy.
The Handi has special problems that are not related to the barrel per se.
That is all connection are loose. The latch is the biggest culprit.
The loose fit of the barrel in the action. Big gaps between the underlug and the action. Very poor fit of the forearm hinge piece. These are your accuracy problems and no amount of changing loads will fix that..
We have to counteract the torque of the barrel, the uplift forces on the latch created by the hinge pin not being in line with the recoil forces and the pressure forces against the standing breech and on the hinge pin.
Dampen the barrel vibrations in the forearm. Free floating is ok but it just moves the vibrations back to the action.
All these item put together is what is causing inaccuracy. It is therefore no accident that lighter bullets in a Handi will be more accurate than the heavier ones because of the lesser forces.
In the last month PS Shooting magazine, the 303 forearm (two piece stock) was bedded with RCV Silicone with outstanding results.
L.M Mcpherson came up with that one. Yes his book is good, I don't have one. The trouble with RCV Silicone is that they make 50 different kinds and they don't say which kind they used.
And men, slow those bullets down a bit in a Handi for better accuracy, these are not bolt action rifles.