Sounds like some of the reptile incubators I’ve seen. They usually have an aquarium heater that heats a tub of water and the reptile eggs are nestled in perlite inside of a plastic Tupperware container that is just floating in the temperature controlled warm water.
Sounds like a neat project. Perhaps if you used flexwatt heat tape wired to a thermostat that had a probe, you could put the probe between 2 gallon bags of water that were resting on the heat tape. Most digital thermostats have a <1 degree temperature variance so you could make it so the water bags stayed at a constant 99 degrees. Making sure the bags of water stayed sealed would be my only concern. Using one of those kitchen bag sealers you could Fill up a bag of water and then permanently seal it. Your eggs could all rest on top of the top bag of water.
that’s an idea, they’d need to be hand turned but the concept seems like a more natural way of incubating eggs versus hot air chambers which most incubators are.