Belated update...
The soak and ultrasonic clean worked. It's been running for a 60 minute and a 90 minute sprint today without any surging whatsoever. I might have been able to do a straight two hour test, but the fuel tank dropped below 1/4...
Freshly installed, the cleaned carb smoked like crazy for the first 10-15 minutes. Aside from that, entirely satisfactory.
I also installed a $5 fuel shutoff about 3" from the carb inlet, so that hopefully it never sits wet again. Shut down the gennie after about 60 seconds of closing the valve.
Word of advice... take pictures as you go should you ever try this yourself. It's really easy to lose track of what goes where...