Most carb kits will have all the gaskets you need, but they also have a new float needle/seat.
Check the old ally washer under the needle/seat when you unscrew it, there are different thicknesses available and that's what sets the correct float height (to get the right fuel level in the bowl). From memory there can be 0.3mm thick, 0.5mm thick, 1mm thick, etc, put the same thickness out of the kit back in so the fuel doesn't leak out, the ally washers are a use-once-only thing.
You can pull out the float pin (carefully, the assembly is a bit delicate) and to stop the stickyness just get some 1000 emery and lightly polish it until it's shiny again (which means there is no gum or varnish from the fuel left on it), and that will fix that OK.
Throw the new gaskets in it, there are a few options in the kit so check the holes are in the right place, etc, and they are the right size, then button it up and off you go I rekn.
Job well done.
So from that I gather that if the pin was stuck DOWN (open), that would result in flooding.
Where as I was only seeing the pin get stuck (and I use that term loosely) in the UP (closed) position.
Not saying that wasn't the cause, as it's possible it was a freak stuck that has since cleared.
Given as shown in my little vid that there was some ability for the needle to get itself stuck closed, it stands to reason that perhaps it was also at some point stuck open.
Fact is, engine and tank were emptied of all fuel, through the sump, so it's the carby that is the most likely culprit from what I'm reading now.
EDIT: I guess another thing to bench test is, once rebuilt, is the top fuel valve actually closing when the needle is up/closed, or is something still allowing fuel to seep through. Perhaps the needle is meant to even go in further than I am seeing, and hence not fully closing off the fuel supply.