Time to rebuild?

Since fixing the choke pull-off I've noticed that the engine still bogs down at idle shortly after a cold start--not as soon or as badly as it did before, but within about 30 seconds of starting it starts to feel what I would describe as over-choked or flooded. I might suspect the electric choke heater isn't working, but the ambient temperature has been too low for that system to kick in. So it's not the electric choke assist. Also, while this was happening I removed the air cleaner lid and pushed the choke plate open with my finger, thinking that would help. However, opening the choke had no effect (before I pushed it wide open, there was maybe 1/8" or 3/16" gap next to the plate).

I thought maybe my fast idle is adjusted too low, so I raised it a little, but that didn't seem to make much difference. (It's a little hard to tell because I couldn't check the results until the next day, which wasn't as cold.) Could it be the electric choke assist is heating when it shouldn't, and opening the choke too much too soon? Could it be a more basic problem with the idle circuit or the float bowl? I haven't looked at the carb yet. I could try rebuilding and swapping in the carb that was removed from the car just before I got it.