Looks like the easiest config for changing the PS front outlet to inverter may be the residential fridge models*. It would, however mean pulling the fridge, instructions for which are up to somebody else. The RV fridge models work similarly, tho you may have to pull the under-fridge furnace on models so equipped.
The front outlet is chain-wired thru the fridge outlet on RV fridge models; fridge outlet is visible inside the fridge's lower vent cover from outside the coach looking forward. On ResFridge models power follows same path but bypasses fridge outlet which is on inverter.
Power comes in from basement, and goes up the inside of the fridge cabinet (either to fridge outlet or continuing uninterrupted) and into the back of the dinette-overhead cabinets thru their false back (got me how this works on dinette slide models or 38' units). You can see the overhead wiring with cabinet false back removed in Dale's post #1, 5th photo
here.
So OEM front outlet wiring is from panel into basement, up thru floor to (or bypassing) fridge plug, up thru fridge cabinet & across back of upper cabinets, then into wall and down to front outlet.
IIWM, I'd
A) unplug coach, shut off AGS, shut off inverter, and take all other ordinary and recommended safety precautions like hiring a professional who has insurnace and a health plan. Then check power at dinette & front outlets; fix whatever is still sending power to places I'll be working.
1) install 2 new junction boxes, #1 in the back of upper cabinet next to fridge cab (behind false back), and #2 on inside rear-facing wall of fridge cabinet
2) pull feed off dinette recept & route it into #2Jbox
3) cut romex @ upper cab leaving sufficient length & run it into #1Jbox
4) run new romex from #2Jbox to dinette outlet (will be a short piece)
5) run new romex from #1Jbox to #2Jbox* (about 8' more or less including excess for splicing ends)
6) splice romex together in Jboxes as follows:
7) wire nut 3 white, wire nut 3 black, wire nut 3 cu in #2Jbox (3 wire nuts, 3 wires/splice, don't mix colors!!!)
8) wire nut 2 white, 2 black & 2 cu in #1Jbox (3 wire nuts, 2 wires/splice, no mixed colors!!!)
9) wire dinette recept from new romex out of #2Jbox
10) install #3Jbox & push cut end of romex in upper cab (comes from fridge outlet on RV models, bypass of fridge outlet on res fridge models) into #3Jbox & wire nut ends of white & black wires so no exposed copper;
remember this romex will be hot when coach is plugged in or gen running so good termination is essential to safety
11) check applicability of various homeowner's & RV insurance coverages & alter as needed for applicable perils

12) turn on inverter & check power to front & dinette outlets, check polarity,

turn off inverter & fix what I screwed up; repeat till outlets work normally
13) turn on gen & check all outlets,

shut off gen & fix whatever I screwed up; restart gen & check;

repeat as req'd; kill gen
14) plug in coach & check...

fix... check
15) cover all 3 J-boxes and reassemble coach
B) shedule a long, relaxing trip that will make copious use of the new inveter plug

, cuz that was a crazy lot of work for not having to use an extension cord or an alternate outlet.
*for RV fridge models, there is a "floor" to the fridge about 15" above the coach floor & new romex will have to be fished thru this fridge floor. I'm guessing it is easier to push the new romex down with/by the wire bundle that heads up to the upper cabinet, and then fish the upper end w/a fish tape, making use of the lower rear (exterior) fridge cover.
Hope this helps. I talked myself out of it.