The usual cause of a blocked filler cap drain is a kinked hose under the tank, otherwise it could be debris that will probably shift if you have access to an airline.
Emptying the tank is always a pain: it holds a lot and it's tricky to get the last couple of litres out, but it's worth doing to get rid of any remaining water. If there's rust in there, clean or replace the filter and consider lining the tank: I used a kit by a French company called Restom, POR15 is another make of tank sealant.
Draining the carbs is easy, there's a drain screw at the bottom of each one. I fit a short bit of plastic tubing over the spigot and drain them into a jam jar so that I can see what the fluid looks like.