2004 honda vtx 1300 c stalls out after down

Wish I could help but mine , '06 does the same thing. Turned the idle up and it helped quite a bit, but still have to leave the choke on at least 10-15 minutes. New plugs and cleaning the carb did nothing. Gonna try adjusting the A/F screw today.

tap bowl on carb sounds like float stuck in down position,

Sounds like the pilot circuit in the carburetor is clogged or restricted. You will need to remove and clean your carburetor.

Make sure the choke is pushed ALL the way in. If you've been using it, you may have fouled the plugs.

You should check your side stand switch, this will kill the motor