With the water volume you have, unless you add a bunch of huge fish at the same time you should have nothing to worry about. FYI, Alex just got in a nice fat zebra eel, very cool critter and fish safe too. I recently added a small one to my system, he's a favorite inhabitant already. They are a bit clumsy but so far he hasn't disrupted any rocks or corals, and nothing is cemented/epoxied in place.
Your LED lights won't add any signifiant heat to the system, particularly with your vent hood arrangement even if the fans aren't running. Any extra heat will come from the multiple submerged pumps and your large UV unit. I think it is very reasonable for you to pass on a chiller at this time, but by next summer when you will have a substantial financial and emotional investment in livestock, and it starts heating to 110+ outside, I'd seriously consider it as a failsafe.
I primarily rely on central AC to maintain a stable temperature in the theater and fish room. But I did purchase a Teco TK3000, it was not terribly expensive in the scope of the whole system, and hopefully will prevent a disaster should there be a HVAC failure. Unfortunately after a few years, the starter motors and capacitors in the big HVAC compressors do crap out, it has happened on two of my eight Trane units since 2009; I had Lennox in my previous house, and they were significantly less reliable. Usually I can get them fixed same day, but occasionally parts have to be ordered and it takes a couple days. And once fixed, it can take a long time to pull down a room that has warmed to 90+ degrees!
The Teco chillers have a standard dual mode thermostatic controller, and the larger models have four internal accessory compartments. While it won't typically be needed here in Arizona, I did install a 400w heater in one and have (3) 15w UV units incoming for the others; the UV is intended for 'polishing' tank water, not for parasite control, given the wattage and flow rate, but still it's nice to have a 45w unit inside the chiller where it needs no extra plumbing, power supply, or controller.
Regarding backup power, I looked into installing an automatic natural gas backup generator but the installed price was prohibitively expensive and there were potential issues having it kick on reliably when the grid fails, which is the whole purpose of having it. Instead I bought several Icecap battery backups for my Gyre and Vortech pumps, and they should keep the water moving sufficiently and surface agitated for 1-2 days in the event of a major outage. I have experienced a few outages over the years, but thankfully all were relatively brief with duration of no more than a couple hours.