I've been thumbing around about this too. Not happy with the info on the batteries in the Anker. I tried emailing them too, specifically about what type of Lithium was in there. Got the same answer you did. I think Anker is running a bot response.
You could consider just chucking another battery in the car? Depends on how many nights you need it? 100 Ah AGM $160 + $6 for clamps. Seems like it would work real well for 1-2 nights.
Have you tested out the bunk warmer yet? I've got one and just tested a little inside but seems like it might do a real good job cutting the chill on a cold night.
Think there is a way to setup a DC inline timer to have it click off after a few hours but click on before you want to get up? Might conserve the batteries lots.
I've also wondered about the performance of Li-ion in cold temps and if this could be an issue to using one of these power packs?