https://www.iotaengineering.com/pplib/iq4x_spec.pdfLooks like the same charging profile as the IQ4 except four hours at Absorption instead of eight. It still drops to 14.2v 15 min after getting the batteries to 14.6 (It charges at 14.8 to get them to that 14.6.)
Some/many batteries want you to get the voltage up to 14.6 or so and then hold that voltage there to do the Absorption stage.
You can set your solar bulk voltage to 14.8 too and they should add their amps if you need fast charging. Then set the solar Absorb voltage to 14.8 too so you get some quality time there instead of 14.2
Note the input voltage wrt your generator's rating.
https://www.iotaengineering.com/dls55x.htmIt says 950w input, but that ignores the power factor. It says 13.4a at 108v = 1447VA ISTR a Honda 2000 is rated for 1600VA, but the Honda is at 125ish volts. The 1600VA is based on 13.3a at 120v.
The PowerMax 55 amper in a Honda when output is 56.8a when charger is set at 14.8v, on the Kill-A-Watt shows 124.7v, 11.06a, 980w with 1383VA and PF 0.71
So it is hard to say for sure, but IMO that Iota spec of 13.4amps can be ignored and it ought to run ok on a Honda 2000.
The 800w output looks like it is based on the time when it gets the batts to 14.6v since 800/14.6 is 54.79a
With the fat wiring close to the batteries you could might see a few more amps output. Some "55s" will do 60 like that.