Lol, sounds like quite a day! If you can purchase a rebuild kit fairly cheap- you might want to try it your self- plenty of Youtube videos to help, and pay attention to the different settings for floats, etc. Just pay attention to where the parts came from, place them in an easily to remember order, and have a couple cans of carb spray on hand. You will also want some small dia wire or super small drill bits to use as cleaners/ reemers. Do not overtighten screws, it will come back to haunt you - a good snug is what is needed. If you dont want to mess with it, do some checking with local shops and see if anyone can do it there.

As far as the engine staying running - was it dieseling or actually running at same rpm- no hesitation? If dieseling- that's to be expected with all that gas going in the carb like you say. If no hesitation and same rpm like no key was ever turned off- that sounds like a bad ignition switch. Try a quick squirt of wd-40 in there and cleaning it before replacing it.