I think you are onto something, but not all questions are answered yet.
The generator still has to supply the 1708 above its 1600. I don't know if that is a problem for the Honda in real life. So far so good in your case. As noted, it doesn't get used that often anyway. Higher altitudes would reduce that ability somewhat.
On the output watts and the high amps, the 1515w is still quite high. Efficiency is defined as output/input watts. (They ignore PF, but here both PFs are 98-97 say)
Input watts with 1708VA and say 0.98PF is 1674w and 1515/1674 = 90%
I got 102 x 14.8 = 1510w out with 1854w in and 1510/1854 = 81%. The usual efficiency of these chargers is around 85%
I doubt the charger in the Magnum is way more efficient than my converter, but who knows?
The key might indeed be the Li battery. I do know a charger can do better if it is just supporting a battery, such as when the battery is being drawn down by an inverter and the charger (not on that inverter!) is providing input at the same time.
You get more amps from the same charger doing that compared with it charging a battery. ( to current limit) Perhaps the same effect is seen with charging an Li compared with a "normal" battery?
EDIT--BTW, I missed something about Li. I have seen they need 14.6 or whatever so eg, PD makes a special converter that does that instead of their usual 14.4. So why is your setting at 13.6?
OTOH, ISTR the 48v charger was for 54v and 54/4 = 13.5