I suspect that a ferroresonant transformer will have a faster response time than a furnace and should resolve the problem. The advantage over a UPS is that the transformer doesn't need the maintenance of that a battery requires.
<< A ferroresonant transformer, also called a constant voltage transformer, will give a constant AC voltage output when the input voltage varies within the rated input voltage range. Typical response for output regulation is plus or minus 3% for input voltage swings that are within the rating of the transformer. Typical response times are 8 millseconds for a 5% line or load variation, and 16 milliseconds for a 10% variation. Generated harmonic distortion will be less than 3%. >>
http://www.powerqualityanddrives.com/sag_correction_without_ups/
