Do you think this one would do the trick?
Since you are on a Jamma machine, I'm gonna guess it has a 110W power supply. However, it might not be pulling a consistent 110 load. The calculation for battery backup choice is as follows:
1.6 * Wattage Load = Minimum Volt-Amperes (VA)
So even if your power supply is pulling the full 110W then its 1.6 x 110 = 176VA ... and the power supply you linked is a 350VA so that will cover it.
The original unit I suggested is probably overkill but the AVR just immediately popped into my head. Your are certainly right, no sense in spending $100 when $50 can fix it.
I'd buy it locally or borrow a friends first if you can. That way, worst case, you can return it if it doesn't fix the issue. (Make sure the battery is good and charged before testing it out)