A caution is many of the cheap UPS devices also have no isolation, so the battery is connected to either one side of the mains, or is on a rectified mains supply. Treat the battery cabling as if it is mains connected, and put the external batteries in a plastic box suitable for mains use. In the space vacated by the battery put a high value electrolytic capacitor, 10 000uF 25V or so for a 12V unit, to provide local decoupling for the UPS, and use 4mm wire to connect the external battery pack. Inside there is now room to add a 12VDC 80mm fan, powered by the battery, to cool the inside of the unit. Place so the fan cools the transformer and the heatsink of the power devices, and if you have the ability add an extension to the heatsink to improve the cooling, but make sure it does not foul anything.
Still not going to be a great UPS, just a better cheap one, which will run longer. Done that, and it has improved runtime to around a hour, though I am using 10 7Ah SLA packs in parallel, used ones but still reasonable.