Precision, it isn't a surprise you're not having any luck if you haven't yet removed the main jet and emulsion tube. If the main jet is tough to get out, you will need a screw driver bit(preferrably one that is hollow ground, not tapered), that, as nearly as possible, fills the slot in the main jet. Yea, some can be tough but I've never failed to get the main jet out of a Honda carb.
Like Pugs, I have had no trouble cleaning up a Honda carb.
Pick your own poison--what have you got to lose in giving it a shot particularly if you're willing to part with $60 for a new carb.