draining the bowl is definitely a very good idea.
However, my past experience is that using Stabil is NOT a very good solution. It may delay the problems but not eliminate it.
What I have found is that seafoam is a very good solution long term. a) once I switched to seafoam, problems gone, AND seafoam did a great job of "fixing" carbs that had been gummed up after using stabil. A double dose of seafoam, let the engine run at well above idle (honda 2000 turn off eco) 30 minutes later problem gone. idles fine, runs fine.
BTW on the new honda 2200 NO need to drain the float bowl. One off position shuts the engine down ASAP. The other position shuts off the fuel pump and lets the carb run dry.
It's also easy to mod an existing honda 2000 to do the same. a push button to kill instantly, off position lets the carb run dry.
Hutch mountain sells a kit
https://www.hutchmountain.com/collections/amazing-generator-accessories/products/bad-gas-ethanol-gum-carb-eliminator-switch-compatible-w-honda%C2%AE-eu2000i-generator
I've used the Hutch mountain propane/NG conversion kit on my 2000 and my 2200
2011 Keystone Outback 295RE
2004 14' bikehauler with full living quarters
2015.5 Denali 4x4 CC/SB Duramax/Allison
2004.5 Silverado 4x4 CC/SB Duramax/Allison passed on to our Son!