The three fault modes would be:
1) Too low or too high input voltage
2) Too much load on the output
3) Faulty unit
Do you have a voltmeter to measure the battery while in use? Maybe the van alternator is putting out too high of a voltage.
#2 doesn't seem to be the problem if it is indeed a 750W inverter.
The spec sheet for the freezer states "•Power: 67 W / 115 V / 1.1 A". This doesn't add up unless the 1.1A is surge, which seems low. My guess is the freezer is drawing ~120W while running.
Maybe the freezer compressor doesn't play nice with the $45 MSW inverter.
#3. That's where I'd bet my $$$. Your $45 HF MSW inverter comes with poor reviews. I understand wanting/needing to cut corners on a project such as yours BUT installing a bargain basement MSW inverter was not the place to do it. This is where you should have spent the extra $ on a reliable, top shelf PSW inverter. Rethink your inverter choice prior to your next outing.
I'm sorry I can't be more help.