Actually, in the video he connected LiFePO4 and FLA in parallel.
But let's discuss particular situation ...
First you claim, "a LiFePo4 requires a higher voltage than an AGM"
Explain why you can't use 14.4 volts for the LiFePO4 battery?
That looks like the exact same voltage for AGM at 70°F.
You think 14.4 volts is too low for LiFePO4 battery - you are joking, right?
You need to specify the voltage you think is "required" for LiFePo4, because you have not.
Secondly you claim, "you won't be able to utilize the true deep cycle cycles of lithium".
Actually, we can and will get 80+% DOD from the LiFePO4 battery.
The Low Voltage Drop-Out voltage will be that of the AGM.
And the TOTAL amp-hours is the SUM of both battery banks.
You need to do some actual research regarding this issue.
Third you claim, "lithium has a high efficiency of 99% where lead acid efficiency is about 70%"
So what?
This causes no problems.
Nevertheless, you still have not given a single valid reason WHY this cannot be done.