If the hunting is at or near idle speed, you will need to pay particular attention to the idle jet. On the GCV engines, unlike the GXV ones, the idle jet is a pressed-in metal part that has to be cleaned in position in the carburetor. This is not an easy thing to do with a 0.3 mm hole buried deeply down in a coal mine, but it can be done with a jet drill bit and a lot of care.
Don't forget to check the condition of the gaskets on each side of the carburetor insulator, which are a standard source of air leakage on Hondas unless you replace them each time you remove the carburetor.
Other than that, I suggest you look closely at the emulsifier, which is prone to gum formation on Hondas, and it also can be difficult to dismantle due to the gum sticking the nozzle (venturi) end of the emulsifier to the carburetor body. Remember, you need to be able to put the correct size of jet drill bit through every one of those lateral holes. Note that some emulsifiers have two different hole sizes.
I have no respect for bar blades: they bend crankshafts, damage bases, cut poorly, and give a weak draft into the catcher. The best cure (on Hondas anyway) is to get a proper blade plate from a defunct Honda and fit four new good-quality blades to it. I did that on my favourite Honda (an ancient HR194 from soon after production began in 1983) a couple of years ago, and completely transformed the beast. Now if only I'd done it thirty years sooner, and if Honda had given the machine a bigger grass chute.
