Ricci Price.
Lateral and horizontal stringing is the result of poor latch engagement and or poor fit of the action in the receiver. Fitting the latch and installing a stronger latch spring will take care of of stringing.
Real tight groups can,t be had with an oversize barrel, nor with a barrel bore that is smaller in diameter at the chamber than at the muzzle.
0.0015 oversize seems very common together with the groovers that are only 0.002 deep one is lucky to get 1-1/4" groups with any load, and no amount of polishing will improve that. I found the barrel that I have seen are very smooth and require little break in.
For along time I have been puzzled why the oversize barrel. During my visit to the SHot Show this year I talked to the Green Mountain Barrel people that supplies H&R with barrel blanks.
From what I gathered is that the barrel blanks are supplied non stress relieved. When a barrel as such is contoured, chambered, polished, welded etc. the barrel will relax and shed some of the stress outward.
This will increase all interior dimension. The amount varies from end to end depending of how much metal is removed. Granted this will not make the barrel unusable.
Simply put, an economy product. Stress relieving costs money. This is my observation. In a cheap rifle it is no big deal to loose a few feet/sec and a 1-1/2" group it still gets the job done in good style.
I also noticed that the Rossi and the Baikal SS rifles use the same lock up as the H&R but with substantial more lockup force. Though I would not buy neither one. Very poorly designed for scope mounting and ill looking overall.