There was a recall on a lot of the BF series Engines last October the Programmed Fuel Injection starter main relay could crack under thermal shock.
I dont know if it covered your engine but it certainly covered all above
Your fault is very similar to the symtoms we were warned about with the problems increasing until the engine will not start
I received a recall notice from Honda although the fault never manifested itself on our engine. Someone i know with the same engine had a fault very similar to yours but they did not know about the recall until i told them about it. The part was changed on their engine under warranty and it solved the problem
Contact honda to see if your engine was covered