Mex's idea is a pretty good one. A single silicon diode (or rectifier, same thing) has about a 0.7V drop when conducting, and that's mostly independent of the current flowing through it. With appropriate heat sinking for the power it would be dissipating, it should bring the voltage down sufficiently. Using the bridge rectifier gives you two diodes operating at a time, hence the 1.3 volts.
As an additional "advantage", you could hook up the inverter with it to the battery backwards and not have any problems.
I suspect the inverter may have an over voltage shutdown because the output voltage isn't really regulated, and so too big a swing of the input voltage would lead to too big a swing of the output voltage. I could also be all wrong about that.