Hi-
I just had this type of problem with an 1885 Highwall. In my case, it appears to be the "trigger sear spring". This was identified by Browning expert Lee Shaver, who is a gunsmith in Missouri, I believe.
Apparently, all the low walls are also made the same as the high walls, so I just ordered 4 springs from him as I have several. These springs apparently crack over time and he has some replacements that are more sturdy. In my case, adjusting the trigger screw had no effect, and in fact. the gun "fixed itself" temporarily, which is a bit disconcerting!
Lee's phone # is 417-682-3330. It would probably be profitable for you to call him.
Good luck!
Scott