I've had the same problem with an older H&R revolver with a swing-out cylinder (which is probably pretty much the same as yours).
The chambers appear quite smooth, though I guess they could be undersized.
Anyway, I take a well oiled boresnake with me when I shoot it and periodically clean and lube the chambers. That seems to help quite a bit.
You might also want to consider trying standard velocity ammo, if you haven't already.
Actually, what also really works nicely is using .22 Shorts. However, nowadays they are pricey and hard to find.
When things start getting really sticky, I've loaded only six rounds instead of nine, which also helps.
While certainly not a Colt or S&W, H&R's (and NEF's) are surprisingly decent little revolvers for the price. It's a shame they're no longer made.