Altronics/Jaycar have a whole bunch of waterproof connectors that would fit inside the case on the side, like Grim did.
Something like
this? 2A per pin only though.
edit:
Probably even something like
this would fit. 5A per pin, 6 pins. Quite big.
On the other hand,
this D-sub connector has 5A rating, according to the data sheet. I assume per pin???