Battery cost shouldn't be such an issue.
A cheap UPS is truly just a battery backup. The appliances attached draw power from the mains until the mains power disappears, then a switch causes the battery power to come online. If this doesn't happen quickly enough, then your pc might hibernate. These types of units tend to provide batteries delivering up to 750, or maybe 1000 amp hours (from what I can tell). An expensive UPS of the "inline" variety might provide a battery of 5000 amp hours. Now, these batteries are likely to be EXPENSIVE! But for an audio application, there would be no need to use such a big battery, since the battery life is never a real issue (unless you're committed to the idea of listing to your system during a power outage). So the idea would be to find an old "inline" unit, where the battery has died, and replace the battery with a deep charge 12v car battery (which might cost you $50-$200, depending on the technology you like).
The issue of producing a nice sine wave might be more of an issue. I know that the types of inverters used in these applications are marketed in different ways - some of them produce a "modified sine wave", and others claim to produce a "true sine wave." It seems most use something called "pulse width modulation" to produce a wave - I have no idea what this is or how accurate it could possibly be. However, if PS Audio is charging in excess of $1000 for a "power regenerator", where the difficulty lies in producing a perfect sine wave, I'd be prepared to believe that these inverters may do a shoddy job.
It's clear though that there are many applications where the good sine wave is important. For example motors run off modified sine waves will be prone to break down, which becomes important for those of us who would like to use the power to run water pumps in an aquarium when the AC goes out. So some technology is invested in sine wave production.
Chad