I wouldn't do it, personally. For one thing, batteries have different capacities, for both output and reserve power (how long it can keep your equipment powered). You'd have to match those up with whatever APC provided. For another thing, your UPS probably acts as a surge protector, too. You have a lot of 5-year-old components which have absorbed the shock of electricity from your power company (some of which is more stable than others). They've done their time and they should be replaced. Finally, there's no guarantee that a replacement battery would fit where it's supposed to. I don't know about you, but even with as much computer gear as I have around the house, a marine battery will not do much for the decor. :-)

One option for you is to go to APC's Website. They give (or did, last time I checked a few months ago) current owners of APC UPSs a "trade-in" discount on a new UPS. Between shipping yours back for proper disposal and the discount they give you on a new UPS, it may not be the steal of the century. But you know you're buying a quality product (IME) and disposing of the old battery properly.

I saw the trade in discount on their site.
It didn't look like a good deal to me.
Basically I could trade it in for a like model that costs the
same as this one did new (~$100). And that's with the discount.
They will send me a new battery and free return shipping on the old one.

My UPS is also a surge protector. I don't know what your definition
of unstable power is but I would say our power is VERY unstable.
I got the UPS after the power went off 17 times in one day.
And every day we get blinks in the power.

My original idea was to get a marine battery and let it sit here
fully charged and use a power inverter. If the power went off I
could just reach over and unplug the UPS from the wall and plug
it into the inverter. I may just stick with that plan.

Trust me, a marine battery wouldn't be noticed
in the piles of "decor" I have around my computer space.

My biggest concern was with the idea that a bigger battery would
be too much for the charger to keep up with.

Pooh Bear

Well, if you size the marine battery close to what APC supplied, I imagine you'd be okay. You're kinda cooked if the failure happens while you're out of the house, but maybe you don't keep your computers on full-time like I do.

AFA "stable" power, I've lived in places where the bulbs got brighter and dimmer and fans speeded up and slowed while you did no more than watch them. I have incandescent bulbs in my house I haven't had to replace for years -- IMHO, that's stable power. Unfortunately, not everyone has it.

Nope, my computers run full time.

Our power levels are stable, but are either on or off.

I'll just have to get an OEM replacement from APC I guess.

I would love to have a home NG standby generator.

Pooh Bear