I'm not going to be much help here, but....
A friend of mine and I were re-wiring his trailer. Now, keep in mind I'm not an AC guru (barely amateur). The way the trailer came was it had one set of outlets like in the Chinook. Then a completely separate set of outlets for the inverter. Talk about a pain: You had to go around on hands and knees un-plugging and re-plugging everything depending on what you were doing.
So part of the project was to put in new AC and DC panels, new/different inverter, better charger. BUT, unlike his previous RV, which had a big whole-house inverter/charger, he was going with just a plain inverter (but just upgrading it a tad from the original, which was tiny, because we also put in a bigger/lithium system.
So okay, let's get rid of that crazy separate outlet system. Yes!
But it wasn't so simple. Because if you just put the inverter on the same outlets, then as you have figured out the inverter will be in a "loop" where you don't want it (sorry, I am bad at explaining this part, but I think there were bonding issues and something else too (WHY I can't describe this; I don't know but I never can). This would not be a problem with a combo inverter/charger (which has its own switching) but he didn't want that because he only uses the inverter once in a blue moon.
My buddy is a little on the, well not lazy side, but let's say go with the flow side. So he decided just to keep the separate outlet system (also, he only uses the inverter once in a blue moon, so that helps).
But another fellow with the same trailer used a (IIRC) 5-pole switch to make and break all the appropriate connections so that shore and inverter could be on the same set. It was this type, I believe (but I think it had five poles?)
https://www.bluesea.com/products/8366/A ... OFF_2_Pole
I can't remember the brand name of these right now, but they are not actually made by Blue Sea and you can get them without the panel plates for less money elsewhere. I think it was a German name (would look it up but on way out door).
Blue Sea also makes AC panels with manual selector toggles - not sure if that would work plus those are $$.
But maybe your relay way is actually better and cheaper? I'm kind of out of my depth. I only posted because we did run into that exact same issue, and while my buddy decided to just keep the separate outlets the other fellow did use one of the switches I showed to make it all work.
PS: I just spent ten minutes searching for that fellow's post but I can't find it and I have to head out now.