Our church gym has a large gas overhead heater that requires a reset every once in a while. Of course, the button is on the top of the heater, which means a trip up a fourteen foot ladder each time it needs resetting.

Would it be possible to wire a reset button in a reachable location?

No this limit trips when the flue gases don't vent. Try extending the flue on the roof a couple of feet this usually solves this problem. The unit is a natural draft type furnace the flue pipe has to heat up before it will draft.