From the sounds of things you have a power problem either too much draw (high wattage on the bulbs) or low quality switches and cords. Are you plugged directly into the mains (wall) ? or are you using an extension cord?

I hate suggesting someone mess with a heating system that is working out for them, but it sounds like that might be something you may want to think on.

There is not much evidence about how important a day night cycle is or is not. But there is certainly nothing wrong with having one.

I will describe my system I use and perhaps it might spark an idea for something appropriate to you.

In my enclosures I have a UTH (stick on thingy) that provides the primary heat. I am in a cool environment and the room temps are also quite cool my solution (MY is not yours this is what is working for me take what you will from this) is to add a second uth to heat the cool end to where I want it. Both are on thermostats.

Ok so lighting, I have a (18 inch) fluorescent light inside the enclosures. This helps are great deal with increasing the ambient temps the bulb doesn't get super hot (like a regular bulb) but it still gets warm. (make sure the snake cannot lay against it touches are ok but long term contact might be a problem) This runs for 12 hours or 'daylight' it is just a regular cool white bulb not a high uv bulb. I have a dark blue LED light string for 'night' lighting so the night light comes on and there is a bit of over lap and daylight goes off. This also drops the ambient temps some (4-5ºF) but the hot spot and cool spot is maintained.

Day temps are 90ºF cool is 80ºF ambient air starts at about 79ºF and gently rises to about 84ºF after about 8 hours. night temps 90ºF and 80ºF The ambient temps hold around 84ºF maybe 85ºF for about 3 or 4 hours then start to decline to a early morning low of 79ºF then it starts over.

The fluorescent lights draw 8 watts and the LEDs draw well 1w maybe 2. There is no heavy tax on switches or cords and there is not a heavy draw when things come on and off.

Do you room lights dim when things in your set up change? it might be poor wiring in the house too. Surges may cause bulbs to burn out early.