If you want to go away from bulbs, want something that is a set and forget AND something to look after thermostat + egg tuner duties, then I would look at something like this.
http://incubatorwarehouse.com/225-watt-cabinet-incukit.html Scroll down the page and it lists it's goodies and there is also a video that walks through the set up.
EDIT: Here is the updated video as the one on the page is the older version.
I am sure there are other models out there, but I have this ones little brother, and I can honestly say, once I was happy with it's set up it took so much stress out of parameters of hatching. Some say that's the fun part, but if you want this to be turned on and no worried about then something like this would be my pick.
Would still need something like that relay to make the actuator you have work, or you could look at picking up a rotary motor and set it up like that turner video I posted in your thread. If you did swap it, that actuator would not go to waste, you could use it on a timer for a sky light, air vent or pop door, very easy to set up on a three way switch for manual use off a car battery or solar panel.
Keen to see what other systems people may know of for a cabinet set up. Plenty of bright minds on here.
NOTE; Doogie Howser does appear in all their movies, very informative, even shows how to DIY a 'bator for about $20 using Dollar Store parts.