I work on "neglected" Honda carbs all the time and sometimes I find that it is easier and less costly in terms of time spent (I don't work for free so labor charges add up) to just replace the fuel bowl and "jet set" tube as they can be difficult to get thoroughly clean at times. Those tubes can get a small, hard particle in them that you can barely see at all and it won't come out UNLESS you have a sonic cleaner. I just toss it.
I've even got a brand new fuel chamber, that I personally unwrapped, with crap PACKED TIGHT in the vacuum passages. Now THERE'S one that will burn you! It sure got me! I chased my tail over that one because I really thought "it can't be the carb, I just cleaned it". I flush all new parts now because of that one!
I don't have access to a sonic cleaner but I have very good success cleaning and servicing carburetors. As hondamech stated, if you are VERY familiar with the carburetor and all it's passages and what they are for then you will see the need for COMPLETE dis-assembly as well as new seals and gaskets, along with needed hard parts, to get them properly squared away.
Many of my calls are for "I cleaned the carb so that must not be the problem". However, it often is.
The "jet set" cracks occasionally too and the upper, tiny little oring that seals the tube in the top of the throttle bore is very easy to damage going back in so extreme care needs to be taken there.
I have posted several times on this forum my method for cleaning and checking the flow of the three and/or four feed circuits in the Honda carburetor so I won't rehash that here. I will reiterate though how important proper storage is to keep from having problems. I don't want any of my carburetors sitting for more than a few days with any fuel left in them. So, when you get your outboard running right, do yourself a favor and drain the carbs each and every time you put the boat to bed.
Good luck.