Overflowing carbs are still an issue.
Do you have electronic ignition or points? If you have points have you checked on the condition of the spark advance while you were there to make sure it functions properly, are the points new, factory or aftermarket, have you set them properly with a light (on 1-4 and 2-3), are you sure the timing is correct? Are you using a fresh battery or trying to resurrect a dead one?
Have you cleaned the fuel system yet? Tank,petcock,fuel lines...are you running fuel line filters, do you have excess line, is there any hard bends or kinks in the line, are they running on a downward plain from petcock to the carbs and not wrapped around them. Are you sure you didn't get any crap in the fresh carbs from an unclean fuel delivery system.
Sounds to me like the carbs will be coming back out and blown out (at least), at that time you may want to recheck float height on all 4 and possibly change jets ( your call).
Are you going to purchase another wiring harness or will you take those crappy crimps out, solder the splices ,and shrink wrap each repair?
I would suggest doing only one of these things at a time so you can isolate the problem/problems starting with the fuel delivery.
And I didn't ask before but, is this fresh gas or gas that was waiting for the lawn mower, there hes been issues with shelf life on fuel.
Just trying to get a better picture of where you 're at exactly.