Diki, I have been using inverters for more than 20 years - never had a problem with anything frying or under-powered. Most have built in voltage regulators to prevent such problems.
As for lugging around a lead/acid battery, my garden tractor battery weighs less than 10 pounds and has no spill caps. When I had to use an inverter for an outdoor job, such as a remote mountain campground where there was no electricity available, I just plugged it into my cigarette lighter connection in my van, then ran an extension cord from the van to my keyboard setup - nothing could be easier and safer.
Good luck, on whatever you decide upon,
Gary

_________________________
PSR-S950, TC Helicon Harmony-M, Digitech VR, Samson Q7, Sennheiser E855, Custom Console, and lots of other silly stuff!
K+E=W (Knowledge Plus Experience = Wisdom.)