APC makes some of the best UPS's on the market and should have a solution for you. Many of them have power cleaners on them as well which may be of some interest to you because of the power problems you have. They are expensive though, but are well worth it.
The 600 watts you are using should be more than enough to power your PS3 for a few minutes. After a while the batteries will stop holding a charge. A strong power surge can stop the device from funtioning properly as well.