2006 VNL 670: Operating shore power outlets on inverter power

Looking for some guidance as I finish up restoring my truck so I can get out of the loaner I've been running to stay afloat. It's equipped with 110V shore power but no factory inverter, and I'm hoping to use the shore power wall outlets to run my fridge and my microwave. For hopefully obvious reasons, relying on shore power for those is the polar opposite of ideal.

So while I have the interior pulled apart from replacing my floor, what with this being the perfect opportunity to add/rearrange any wiring in the sleeper, does anyone have any advice as to how to go about tying in the shore power system into an aftermarket inverter, such that I can functionally use either as necessary until such a time as I can obtain and install an APU?

Thanks in advance.