caseyq.
There are not many Handis that will shoot that bad, two in in one place no way.
There is something loose and changing ammo is not going to cure that.
Scopes can be notorious bad actors, try a different scope. While you at it
remove the scope base, clean the screw holes and glue the base down with J-B Weld, but don't glue in the screws.put some oil on them.
Once the glue is set remove the screws and remove the oil from the holes and screws apply blue removable lock tight and tighten the screws into the clean holes.. No more loose base. Some bases come from the factory with loose screws.
Gluing the base down will stiffen the chamber end and lessens the vibrations created by the cartridge discharge, not much but every bit helps.
If you are handy you can fill in the base overhang with Devcon steel and drill and tap another screw into the barrel for more rigidity.
Check the scope ring screws and apply lock tight to the rings.
See if there is anything wiggly in the lookup and the standing breech.
Check the latch engagement.
Check loose forearm hinge. You may need a thin spacer between the hinge cap and the wood.for the forearm to make solid contact. Remove the wood screws and glue the hinge cap to the wood, with the spacer if you need one.
Free float the forearm with an o-ring.
Check the stock bolt with a (9/16??) socket wrench. Stock wood shrinks and creates a loose stock, bad news for accuracy. That bolt has to be real tight.
Check the trigger for trigger pull weight.
Now you can try some good ammo, like the one that Mac uses.