A little further investigation indicates that switching power supplies (most of ours are) do not work well (or at all) with "modified sine wave" inverters. Looking at oscilloscope traces of some inexpensive "pure" sine wave inverters they are more accurately "poor" sine waves. Most UPS are...
As an example my charger (Levo SL) is specified as 100-240 V at 2.5 A max. I would expect the max is at 100 V so at 240 V maybe it takes about 1 A. That's still about 240 W and if the inverter is like most and slightly inflates the numbers it is getting close to the limit.
300 W at 12 V is...