We're running SimpliPhi LiFePO4 batteries, and are very happy with them. We're 48V, but they do make 12V models. You do get all the rated capacity out of them, and a bit more according to other users, but I haven't tested that myself and have no plans to run them below 20% SoC.
Peukert's Law doesn't really apply, and they're altogether much, much better than the lead acid bank we had before. Maintenance free, no heating up, no worries about spills or offgassing, etc. They've been truly "set and forget" and have never disappointed us in any way. You can't really determine SoC from voltage, so you need to invest in a good shunt that monitors kWh in and out.
We have six 3.8kWh batteries, or 22.8kWh total. 450AH@48V is comparable to 1800AH *usable* in a 12V system, or 1440AH at 20% DoD. The bank weighs ~480lbs. You have around the same capacity (1740AH) in your system, but can only use about half of it, and your bank weighs over three times as much. If I were sizing your bank, I'd take the 870AH that you currently have usable, multiply by 1.2, and come up with a 1044AH figure. Then I'd try to find a combination of LiFePO4 batteries that provide that in the budget and space permitted.
You might can charge Lithium batteries but need to make sure your charging sources have the correct charging profiles according to the manufacturer's recommendations, in order to get the maximum energy, life, and warranty (if that matters to you) out of them.
You didn't ask about them, but I am not a fan of EV batteries in RV applications. In my opinion, you can't sufficiently mitigate the associated risks and issues. I know of a few people who went that route initially, and moved to drop-in LiFePO4 batteries for peace of mind and reliability.
Building your own batteries from imported cells is an option, if you trust the supplier to actually give you quality LiFePO4 cells, and if they're name brand cells that they're not counterfeit. But I really like my drop-in SimpliPhi batteries that are purpose built for the application and have a ten year/10K cycle warranty.
