We ran a system very similar to what you have for several years. It was 260ah of Trojan golf cart wet cells with a Blue Sea charger and Samlex 1500 watt PSW inverter. We had 200 and then 300 watts of solar of glass cells permanently mounted on the roof. We have even before then had a compressor frig, which was an Isotherm 3.0cf model.
We were able to run the microwave until the low voltage would kick out when the batteries were below 50% SOC. We could go about 3 days if moderately careful in horrible sun. We only had to go for a drive once after 3 days of heavy overcast and drizzle in a semi shaded site at Devils Tower Wyoming.
One thing that I think, some others don't, is that the idea of a true drop in lithium to replace lead acid is really a statement that has a "but" attached to it. As in "but, you can't let them see high temps like they can in side pod or uncooled unbody installs, you can't charge them when the batteries are below freezing, you can't let them go to total discharge, you have to be careful to not overcharge them, you can't ignore getting them to balance regularly, you have to provide for a BMS lockout reacivation method, etc.
Depending on where you live, how you camp, etc some may not need to be addressed, others might be needed. Lithium certainly has some advantages, but not nearly, IMO, as many as the sellers claim.
Less weight per amp hour, absolutely true.
4-10X the number of lifetime recharge cycles, probably a very gross exaggeration as they seem to last about 7-8 years in systems we have seen so far which is similar to good AGMs.
Faster recharging at 1 to 3C charge rates compared to .2C for lead acid. Most of the current lithium specs recommend .2-.4C charging with some going a bit higher. Very few at 1C even. The taper current at near full charge does happen faster in lithium so may 1 hour or so instead of 5+ hours to 100% full with AGMs.
Don't need to charge full all the time. This is very true and midrange charging is great with them. The problem is that most drop in batteries require you to change full get the necessary cell balancing to activate and that negates any midrange improvements for many users.
I often get asked if I would do the lithium sway again, now that I know more about how it all works, or doesn't.
When we did the swap, lithium was dropping but still expensive. Lifeline AGMs would have been about $2400 for 440ah and the 618ah of SOK lithium was about $3000. The lithium install, to work like I wanted it to took nearly $1000 of other parts and probably 75 hours of work. The cost didn't bother me then or now because the whole thing was basically written of as an educational project and they are never cost effictive.
Would I choose to do it if knew what I know now, yes I would. Would I do it differently now, yes I would and I have been playing with more cost effective and easier to install and control ways ever since as that is my nature with projects. My current thinking is that there probably is a way to use simple, non smart, components to do the job at least as well, maybe better, then our system turned out. I doubt I will do it on ours, which is working very well, but it is an interesting thing to think about.