How does supplying a DC motor with lower than rated voltage affect current draw?
So I should be looking for relays with a rated current of about 25A?

You are currently running a 14A motor through 6A relays.  They aren't going to last very long, especially since a motor is an inductive load.  You need relays rated for at least 14A inductive load.
In practice a motor can draw a much larger current when starting up, than when running.  So don't even assume that the maximum current draw is 14A.  Your little 7Ah battery isn't going to last very long either.