My '05 dodge has the same 136A alternator. I have a 440 Ah AGM battery bank. We ski > 70 days a year using the TC, as well as a 3 week ski road trip each year.
Typically use the Honda generator to charge the batteries with an 80A converter when we are staying in one place. Re-wired from the truck alternator lug back to the TC and then returned to truck battery negative terminal using 2 AWG wire, a 150A Mega fuse, and a MOSFET solid state isolater (no real voltage drop).
If we will be traveling in the next day or two we use the truck alternator circuit to recharge the batteries instead of the Honda. Seen 80A initially at 14.4 VDC go into the battery bank when 50% discharge. Been doing this for 10 years on original alternator (275k on the truck now)
While the ECU on the Dodge is suppose to be a 3 stage charger, with temperature compensation, mine just sits at 14.4V most of the time. So I put in a Blue Sea battery switch in the TC to close the circuit once my bank is charged up, to prevent over charging when driving all day to a distant ski area.