If you carefully read the spec's for a/v "line conditioners" - all they do is filter EMI/RFI and control power surges. As you noted, you have a condition (however caused) that creates "power sags" or low voltage conditions.
I live in what once was a rural area...now it's cluster subdivisions and the power infrastructure is the same. During the summer, when A/C use is high, our power can run at around 105 or 106 volts.
I purchased a refurbished APC SmartUPS 1400 (current model is 1500 volt-amps) precisely because it had boost circuitry to handle power sags and enough battery backup to allow me to turn off my equipment in an orderly manner when power failed (about once a month ! ). I also specifically choose the APC SmartUPS line because when the unit goes on battery, it still produces a pure sine wave 120v output. Most inexpensive back-up style UPS units produce a "modified square wave" AC output - fine for computer switching power supplies, but can cause overheating in transformer based a/v equipment power supplies.
http://www.refurbups.com/Catalog/APC-Smart-UPS-Tower-Specials;jsessionid=0a0101421f43585ed47df7f846cbb4b8a787e91d64ac.e3eSc3iSaN0Le34Pa38Ta38Nax90
Plan to change out the batteries every 3 to 4 years - the internal lead-acid batteries just don't last longer than that.