I've had good luck by just creating air some pressure in the line. This can either be positive air pressure from the inside, or negative/vacuum from the outside. It's usually algae, and "gunk" clogging them and keeping them from draining. I think your vacuum suction idea from the outside may work well if you can get a good seal. It shouldn't take a lot of pressure to do the job. Unscrewing/removing the scupper flap is also a good idea to give you access to cleaning.
