You're right...it could be iffy, especially with AGMs which can take a lot of amperage for a long time.
Several posts on this and other Boards have been by folks using the DLS-75 and the EU2000i, but I believe they were with flooded batteries. Typically, charging amperages with flooded batteries scale back relatively quickly and, of course, they won't accept anywhere near as much amperage as will AGMs.
Note that the Iota specs are at 108 volts. Adjusting for 120V, the maximum draw of the DLS-75 is somewhere between the Honda's "rated" output and its "maximum" output (2,000 watts). So, I would guess that the Iota DLS-75 would place a pretty heavy load on the Honda and, with 50% discharged AGMs, it would likely be for an extended period.
Temperature plays a part, too, as output declines with high temperatures. So, if you're going to use the EU2000i as a power source, you'd likely be better off with the DLS-55/IQ4 which would be fully within the EU2000i specs.
JMO...would appreciate hearing from anyone with real-world experience using Iotas and AGMs and Honda generators.