I just picked up on something I didn't mean to relay to the problem. "Horizontal"! The rifle throws the shots everywere, like a bolt action loose in the stock. I believe harmonics is the key here, but harmonics is a funny thing. Stress in a barrel can cause this, but this seems common in Handi from my reading here. The rifle locks up tight, but like the first shot is the good shot. No way should a single shot start throwing shots 4"s after one shot. Do we need to start over?
Yup that little tid-bit changes ALLOT!!!
Now it could be and likely is a number of things!!
Start with the basics... Assume NOTHING!
Is the stocks tight?
Does the stock bolt protrude into the action so it contacts parts?
Is the latch clean and dry?
How is the lock up?
How is the forend fit? Tight loose somewhere in between?
Is the rifle being snapped closed or gingerly closed? (Consistency is key)
Is SAME ammo being used? Is it reloads or factory?
As suggested look at the barrel, start with a CLEAN BARREL! How does the crown look? How is the fit to the receiver? How is the headspace?
How is the trigger? Very heavy trigger is very detrimental to accurate shooting. ESP with new shooters!
You said the scope is properly mounted. ( I would do it over myself after thou roughly cleaning the threads and holes. Then use lock rite AND slow 24 hours MINIMUM before shooting! Mount a KNOWN good scope.
When shooting try it without forend. Look for differences.
Allow the gun to completely cool between shots. ( we are looking for the problem here.)
Be sure the rifle is properly rested. You do NOT any it shot off a hard rest. When resting the forwards rest should be at or close to the hinge.
Be sure the trigger is completely pulled to the rear.
Good luck!
CW