Lithium VS AGM

Isn't the inverter on the draw side of the system, and the alternator on the charging side?

 

From what I gather and probably wrong is,
A lithium battery at 100% is 13.3 volts and a lead acid or agm is 12.7 volts at 100%.
So if you charge an agm on li. setting it will overcharge the la or agm.
conversly if you charge an li battery on agm setting it will not fully charge.
so the ah number will be''off''

 

I have a thread on my Lithium starter batteries. I’d go with them if you have the money.

 

Ionic Lithium 12V Group 31 3000 CA LiFePO4 Heavy Duty Battery

 

I have a 1991 379 with a 893ci turbo i6 (3406b). Four 1000 CCA batteries supplying the starting power. I'm in Florida so winters aren't too bad. But there have times I need a jump to get started.
Now I have a small lithium battery powering a trickle charger to keep my 4 big ones at 13.4v overnight. Turns over like crazy every morning. Lowest temps so far were about 40°. But I believe this may be something that would help you.

 

Kind of funny you talk about slow starting at 20 degrees, but lithium starters will be damaged if you don't warm them before charging at that temperature. Sure it can be as easy as running the lights for 10 minutes, but they're not good for the cold. Are you sure your system is segregated? I think a lot of trucks with APU batteries just use all of them for the APU but have half under the step. It would be rather complicated to separate them for starting/APU then reconnect all at different voltages to charge. If they don't separate then you may see issues with starter (not deep cycle) in half of the positions and regularly over-discharge them.

As mentioned charging lithium is a bit tricky, but mostly because they'll take all the amps you can throw at them, and that can be bad for an alternator that doesn't self limit. They should charge fully just fine at the typical >14V output from most alternators since fully charged is 13.8V. Also the BMS in the batteries will likely cut current instantly when it senses they're full which can lead to a blown diode in the alternator when the voltage spikes.