The eggs don't need to touch the water if it's a (mostly) closed system.

If you consider the entire system as a whole (water, air, eggs), more eggs means more of the heat applied to the system goes to the eggs, which means less available for the rest of the system including the water, which should cause the water to boil off at a slower rate. If the water is meant to act as a timer, then you'd need less of it corresponding with the slower boiloff rate to result in a comparable cook time.