Having trouble keeping the cool side cool

I would say unplug the uth and continue using the light until you get a tstat for the uth.

You could also add a dimmer to the heat lamp so you could control it. That would let you adjust it although if you have 85 on the cool side and 90 on the warm you don't have much to worry about at the moment. Now if it gets any warmer you may and at such a time it would be nice to be able to turn down the lamp.

If the ambient temp is ALWAYS between 84-89 you do not need to provide supplemental heating at all, but it will not hurt as long as that supplemental heating is being regulated by a thermostat.

So what I'm gathering is I should ditch the lamps completely and get a regulated UTH. In the mean time, does anyone have any tips for me regarding the cool side being warmer than it should be, or is it ok to have it around 84 degrees? When I'm home I can run the air and cool it down to around 78-80 but when I'm working the temp will be higher.

84 is fine

Thank you everyone!!!

I would unplug all heat sources and get a tstat for your UTH. The ambient temps in the room are fine for your snake. They don't need the temperature gradient if the ambient temps remain ok. The UTH, once you have a tstat, will create a hot spot which your snake may use occasionally, may use for digestion only. Until the summer is over and the room temp drops you will be fine without it as long as the ambient temps don't drop below 78-80 or so.

BPs also don't require a day/night cycle. The natural light that enters the room is perfectly sufficient, as BPs spend the majority of their time hidden away from light anyway.

It is very important to regulate ALL heat sources with a thermostat (for the UTH/UTH and light) or dimmer switch (for the light) at the very least. Without regulated heat the temps can spike and anything from a mild burn, serious burn, through being fatal is a possibility. Unregulated heat sources are basically ticking time bombs for your snake. It's not if, it's when will something happen?