The problem here isn't the actual capacity of the UPS, it stores orders of magnitude more power than you actually need to run the Pi for that amount of time. The problem here is massive overkill.
The UPS itself is using almost all of the power, between it's control systems, battery monitoring, communication, as well as the absolutely abysmal efficiency you will get from a sine wave inverter being run with such a small load. Most of the power from the batteries is simply going out as heat before it gets to the AC outlet.
The answer is a far simpler and more efficient UPS system tailored to your needs. Luckily this problem has been mostly solved for you already.
That's pretty much exactly what you need, it handles interfacing a Lithium Ion battery to the Pi. It will take power from the Pi when the Pi is powered through USB, and give power to the Pi when there's no power coming from it. It handles converting the voltage to and from the 5V the Pi supplies and requires, to and from the battery voltage that varies from 3.0 to 4.2V depending on it's state of charge. It also controls the charging of the battery to keep it from being overcharged, and can provide some status information to the Pi through GPIO.
The next thing is sizing the battery correctly. Let's say the Pi is pulling 1A at 5V, that's 5W. Multiply that by 15 hours and you need 75Wh. The conversion to 5V from the battery is at least 85% efficient (more like 90), so 90Wh or so should be enough battery. Lithium Ion batteries are capacity rated at a nominal 3.6-3.7V, so 90Wh/3.65V=24.65Ah.
To get this capacity I'd go with 3 10Ah tablet batteries connected in parallel. That's going to give some reserve and plenty of time before the cells degrade to the point they can't provide enough capacity anymore. You should be fine for a couple thousand cycles at least. 3 of those cells should set you back less than $50 if you shop around. Example ebay listing below, but these are something you should be able to source locally without much trouble.
https://www.ebay.ca/itm/3-7V-10000mAh-L ... 3987810100
It's a much more efficient way to handle the whole process than what you're using now. The Pi doesn't need high voltage AC power, it just needs an Amp or 2 of 5VDC. You're actually spending a fair amount on electricity running things through a giant UPS that drains itself daily, your overall efficiency is probably in the single digit %, not to mention the poor batteries will not tolerate being cycled daily for long if they're the lead acid type used in most UPSs. Lithium tablet batteries are designed specifically for that task.
I've used the Pi UPS board in a couple of projects, one as a short term (2Ah) UPS to provide a graceful shutdown when power is lost and another for a portable media player with a similar size (20Ah) battery to what you'd need. It seems to be built with reliable power handling components, there are other similar HATs out there.
Also saw this thread, might be of interest if you decide to go with the Pi UPS setup. It's really not relevant to your current setup because the Pi isn't currently the main consumer of power
https://www.raspberrypi.org/forums/view ... 3&t=208110