No, I've got FLA deep cycles.
Like you mentioned, the main problem with the WFCO charging behavior is I have to run the generator for a very long time to mostly charge the batteries.
I'll repeat that "mostly" charging them is very nearly fully charging them.
It's not as linear as a lead battery.
13.6 volts / 4 cells is 3.4v per cell.
Take a look at just how full that is based on this chart (and many others just like it).
These things drop a couple tenths of a volt very quickly then remain fairly stable until they suddenly drop off again at the end.
At 3.4 volts per cell you're certainly >97% full with most charts and posted results indicating its actually >99% full.
Take this user's measurements for example.
Hi guys, I was looking through the mobile-solarpower.com website, and on this page I found a battery voltage chart for LiFePO4 batteries. But I noticed it wasn't showing the exact voltage ranges that my battery data sheet does. My data sheet shows 100% charge at 14.6V and 0% charge at 10.0V...
diysolarforum.com
At 3.38v per cell they are reporting 99% SOC. That's 13.52v if each cell is perfectly balanced.
Much to do about little to nothing if you ask me.
Regarding charging speed, if your panel is putting its rated 40A into your system then that's all it's got. Increasing the voltage from 13.6 to 14.4 will speed it up slightly, but it's not going to be a dramatic improvement.
Further, if it is putting that into the battery (the lithium should have no trouble "pulling" it) it should automatically switch to 14.4v anyways, but again this is something I'd need to test out - and I will do so in the next month or so hopefully.
If it does do that then using the lithium specific one will not improve that unless it's rated for more current, it will just improve the charge quality a bit.