Basically, what you're saying is that you don't want Eevee to evolve before the first Gym (although most of its evolution options aren't available yet anyway). Do we know of something else that prevents evolution? The Everstone?
In the same place that the Everstone does its thing, you should add a copy of it except for it applying to Eevee while a particular Global Switch is off (rather than checking the held item). This Switch should be turned on once the first Gym has been beaten. Luckily, you'll be using such a Switch anyway to unlock the next path, so just use that one.