I am having trouble finding battery powered heaters online

The Amp hours needed to power an aquarium heater would drain any sump pump battery in minutes
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In fact in 2000, I used a couple of series 24 Deep Cycle RV Batteries and a 800 watt inverter for my Aquarium Store. We had a major blackout in 2001 and were able to run all our electronics (cash registers, etc.), pumps, lights (no heaters, air though, but then it was summer in LA). This ran fine for a few hours with a full load when power returned. What was interesting is that mobile 24/7 radio reporter for LA station KFWB was driving down the street we were located on and noticed our business was still functioning while others were in the black, and interviewed an employee of mine who showed them our system.

BTW, the Azoo continuous run pump I sell has an AC motor (at least it appears so when I took it apart since it uses a vibrator motor which require alternating current to function), so this pump is essentially an inverter as opposed to a converter (or DC switch). I should note that I only took apart the pump part, but I think this is a safe assumption.

I was out of town for a few days but had a few minutes this morning to capture some waveforms. I used an old scope and a simple resistor network to divide the voltage down to something that wouldn't overload/damage my scope.

This is the way our normal 115vac right from the wall appears or when the UPS is plugged into the wall. As you can see, it's not a perfect sinusoid (could be to the various loads on it) but it's pretty close to a pure sinusoid:

This is the output of the UPS when unplugged from the wall and using it's internal battery-powered inverter:

I also had an old Tripplite inverter in my pickup truck so I hooked it up to a 13vdc power supply and looked at it as well:

72 Hour Emergency Fish Tank Heater for $1: 12 Steps (with Pictures)
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As you can see these inverters are nowhere near sinusoidal output. They call them modified sine but the approximation is really, really poor. I was expecting (or hoping to see) small stair-step approximations but this is only slightly better than a square wave. The only thing that makes this slightly better than a square wave is the duty cycle (amount of time waveform is not zero per cycle) is a lot lower than 100%. It is no wonder that the ac motors don't like to run well off of these inverters. I understand from talking to APC tech support that they make a SmartUPS series that has sinusoidal output (but is also pricier). I think I can do better by getting my own sinusoid UPS and battery combination; I'll report back when I get around to this... But in the mean time, I'd steer clear of general run-of-the-mill UPS types for aquarium back-up power as it's likely to be a big waste of money and time.

Although I have never "scoped" mine (I do not have one, but my Dad does, so maybe he can check his someday), I have not had issues with my Tripplite heavy duty modified sine wave inverter that is hard wired into my camper.
I did have problems with a cheapie one purchased at Walmart than connects to a cigarette lighter or clips to the batteries.

My understanding is that the modified sine wave is more like the square wave when scoped than the true sine wave.

Please see this article from an online RV Blog I subscribe to:

Likely there are differences in quality, as I had similar issues with the cheapie Walmart inverter of similar cost to yours.
Where as the heavy duty hard wired unit cost me $400 (although this price has come down since I purchased as most electronics have)

I take it nothing running in the aquarium requires any power conditioning? I have two UPS' but they're for computers. I could run my off of one of them, but I wouldn't think of running my servers off of a homemade DC inverter.

Power conditioning is always better than none and is easily provided using an inexpensive passive wall strip to distribute power when there is no power outage. The sine wave output inverters we are talking about are not homemade; however they are more expensive than the cheaper modified sine versions (which is really just a square wave with the output suppressed to 0 for a period as it crosses through 0). Emergency Heaters will work with fish tanks 7
Photo provided by FlickrIf you can, get a battery operated air pump to aerate the water.
Photo provided by FlickrBattery operated heater??? [Archive] - Aquarium Forum
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One of the largest choices regards whether you need a manual start or an automatic transfer switch (ATS). Most of us can only afford the manual start option (you get to the pull the string or push the button). However, more affluent aquarists with big tanks or people looking to protect more than just the reef tank such as boiler (for heat), refrigerators (to protect food), some lights, etc may want to consider the automatic transfer switch. The ATS system is just as it sounds. Within seconds of detecting a power outage the generator starts and switches over to provide power and will disconnect and power down when service is resumed. Some of the nicer units include a plant exerciser feature with the ATS. The exerciser can be programmed to fire-up the generator at set intervals (monthly, weekly, etc). This will keep the starter battery charged and keep the unit in top working condition. These systems may also monitor coolant, gas-levels, operating temperature, etc.An aquarium heater uses a lot of power. Something with AA batteries, expect about 15 mins before it kills the batteries. A car battery might last a couple of days, but thats not exactly practical.