I cannot comment on the Handis or Encores never having anyhting to do with them
Well, there ya go.
I side with jedman here. What he's said makes sence too me. Bench shooting and sigting for hunting are two different things. Each require a different hold, even on the bench.
But in no way should the barrel forward of the forearm make contact with any form of support for maximum accuracy. I don't want to begin too explain barrel harmonics here, there are volumes writin on the subject. In a hunting situation will this occure? Perhaps, yet kill zones on game are generally larger than 1" at 100 yards that many seek while loading for and sighting at the range.
I can speak of the Handi specifically, I have 2 that have the forearm bedded at the frame near the chamber, and the remainder "floated" with minimal contact at the lug. This gives me sub MOA accuracy if I do my part.
The Encore actually has a small "button" area on the forward forearm to make a "pressure point" contact on the barrel. This works for some, but others have ground/filed that button off and found better groups. I have a Handi 308 that is giving me fit's,, and I'm going to try a foreward pressure to see if I can bring that thing in.
The break action singles DO have issues all there own, much different than bolt guns. But ya still need to let the barrel do it's thing, un-supported by outside elements, in that micro second of bullet travel.