To increase the UPS's running time you need to increase the size of battery ..
This can be done by adding an external battery ..
But bigger battery also means higher charging current, so you will need to look at the charging section of your UPS ..
Alltogether, this can be quite complex exercise ..
If you replace the output transformer with one rated for higher power you will need to add (in parallel) a couple of power transistors, MOSFETS or BJTs, depending on what you already have inside .. see attached example ..
Maybe you can try to use transformer design sftware ..
Here is one example: **broken link removed**
3.0 - Transformer Design
This next program is thanks to 'Particle' otherwise known as Geoff Sevart. With this, you can either analyse or design a transformer, although for proper design work you need to know a bit more than the program provides from its interface. Although fairly simple, it does give good results if you know what you are trying to achieve, and know some of the basics of the core material.