Update: After cleaning the carb, I put it all back together and started it up. Ran it alright for a bit and cut some grass before putting it away. I don't have complete confidence in it, I don't really feel like the carb was dirty, perhaps I just unstuck something that got stuck with the carb or more likely the auto-choke. I'll do my entire yard this week and update again.
Can anyone offer some advice on how to convert the auto-choke to manual? I'll try and research it.
A few things to consider:
Honda did issue a Service Bulletin last year for some engines with Autochoke. The issue is the linkage can bind up, holding the choke OPEN, making it hard to start a cold engine. The bulletin covered both Honda mowers, plus non-Honda mowers that have a Honda engine. If you'll share the serial number off the side of the engine block with me, I can see if your engine was in the affected range.
If it is, your engine is still under warranty, and a Honda dealer confirms the problem, Honda will update the Autochoke to an improved design at no charge. Again, you must be in the range, still have warranty, and the dealer must confirm the problem is with the Autochoke.
Really would not recommend converting to manual choke. This would require a new carburetor, at least one or more new cables, probably a new handlebar, and if you wanted to have an adjustable throttle, adding a throttle control. Would be a really ugly patch job, especially if your mower was not originally fitted with an adjustable throttle. Finally, converting to a manual choke violates Federal laws related to tampering with engine emission systems.
You can find the engine serial number here; it is in the form of "GXXXX-1234567"