Your reckoning of batteries is sound enough.
I avoid paralleling batteries, preferring bigger cells.
Are these just hobby servos (futaba type)? Those won't take 1A, except, maybe(?) all four in a surge-on, but still.
Try my previous suggestion, go with 2 servos, then add more.
You could make it so over-laden with batteries (capacity) that it can't move, too. 