Alright...learned a lot today!
First off, here are some pics of the engine still in 1 piece.
I pulled the carb out, and dismantled it. I used a whole can of carb cleaner on it, but it still looks a bit green. The bowl is still soaking outside. Should I use a toothbrush on anything to help facilitate cleaning? It appears to be a "PZ-16 50cc Carburetor w/ gold Hand choke lever". I think I'm going to order another bowl gasket. Should I also order the entire 4-stroke 50cc gasket kit? I only need (or can I re-use?) the one for the intake manifold.
I found the screw near the drain line and I think, as suggested, a longer piece of fuel hose propped up will do the trick. That's how it looks in some pics online for ordering a new one.