In sci.electronics.design aurgathor wrote:
I have a 650VA APC UPS (Back-UPS Pro 650)
that has worn batteries (occasionally, it starts to
beep and the red battery light comes ON) .
The UPS is there to ride through brownouts and
outages lasting usually less than 10 seconds (have
quite a few of those) so if the batteries are less
than perfect, I don't care as long as it can last for
10 - 20 seconds.
snip
Alternatively, how would the unit work if I were
to connect a marine or car battery instead of
the manufacturer supplied battery?

Generally, just fine.
If you put a much bigger battery in, you have to be careful of
overheating due to the extended runtime.

Old car battery from scrapyard is a really cheap way.
Altering thresholds won't do much.