Awhile back I did the same. You will need to tap into high pressure for the Generator. I purchased the Hutch Mountain conversion kit for the generator, and asked the same question (about using the current regulator that was on the van to go directly to the Honda EU2200i)...don't recall the details of why, but they said i needed to use the regulator they supplied with the conversion kit.
I didn't have enough clearance to tap into the high pressure fitting inside the door cover to run a separate line. they would have to move most of the hardware (Sportsmobile regulator) to the underside of the frame rail to accommodate the extra high pressure line. Probably what you'll have to do as well.
I deviated a little from this plan since I went ahead and had the whole tank & all hardware replaced - with that process they managed to mount the new tank and allow clearance to run all the lines - cost quite a bit more, but end result was what I envisioned.
You can not run the generator by going through two regulators. So easiest would be to move your existing regulator under the frame rail (because it doesn't look like you have the clearance either), and using a "Y" just prior to that regulator for high pressure. If you do this, I would put another "on-off" valve on the end of the Y & then hose to rear bumper with a quick connect..