Well...it's hard to believe that it is running on just one cylinder...but that is what your description sounds like. What I suspect may be happening is that it is running MOSTLY on one cylinder with the two bottoms probably firing sometimes.
With your description of what you see...plugs ok...coils firing....idle mix screws on two carbs make no difference....but the choke on each does...
...It sounds like gummed up carbys to me. I think you probably have deposits in the low speed circuits of those two carbs and that means the top one is not far behind.
Bottom line? I think they ALL need to come off and get hosed out. That is what I think.
I would also want to know...on an engine of this vintage....what the valve lash is on all cylinders. Although, I still think the carbs need cleaning.
Taking off the carbs can be difficult...but putting them back on correctly...from memory is even MORE challenging. If you attempt this yourself....you need to go VERY SLOWLY and TAKE MANY PICTURES. Having a video camera running might help too. It should be that all three can come off together as opposed to taking them off one at a time.
Cleaning them is fairly easy once they are off but you should have all the appropriate gaskets on hand before you even begin. I would also recommend replacing the three "jet-set" tubes as opposed to trying to get the old ones serviceable again. That way you should have no issues after everything is back in place.
http://www.boats.net/parts/search/Honda/Outboard Engine/0/BF25A LHSA/CARBURETOR/parts.html
In the parts link above you will want to buy all six #22 gaskets....the #38 "muffler gasket"....all three #3 "gasket set(s)"....all 3 #19 "jet-set(s)" and POSSIBLY gasket # 35 gasket, intake manifold IF you take them all off together (the easy way)
I would also recommend buying the #1 "metal anode" and replacing that while you are in there. Especially if you boat in salt water.
If buying all this stuff is "cost prohibitive" for you...it IS possible to do without new jet-sets and the muffler gasket. But if you put it all back and it doesn't run correctly...you will be left wondering if you didn't get one of the jet sets clean enough. WHICH ONE?....Well....that's why I replace them each and every time.
Hopefully someone smarter than me will help answer your questions.