I agree about getting rid of the soiled guts of the cabinet and rebuilding them higher quality.
I think you need your local version of these guys
https://www.crawlspaceclean.com/
I hired them for attic insulation, not rodents, but when they came for the quote the inspected for rodent damage and vulnerabilities.
I know it looks obvious that your particular rats could have walked in the door.
but IMO you should get this sort of professional to do the cleanup AND importantly, to check every inch of your house's exterior for openings they might still be coming in from. for example, maybe there is a dime-sized gap in one of those wire grid things to ventilate your crawlspace, and from there they chewed a path through drywall or the back of a cabinet.
I would pay whatever it takes for an ASAP cleaning service like this to show up today and safely get rid of all the gunk and have experts find the openings and any other nests or damage you don't yet know about. Get this all behind you as fast as possible. Your new house is going to be great but this needs to stop! ugh so sorry!
The timing and logistics of all this is tricky. Pest company says they need to inspect and seal-off areas of intrusion before cleaning up because if you clean-up and the rodents return then you're SOL and the area gets re-infected again.
We obviously want this done ASAP but it's hard finding first availability.
I also have a damage restoration company who I think would probably do an even better job cleaning things up - he's going to swing by hopefully today.
The contractor I found only has availability over the weekends to rebuild the cabinets - I think this is his side-gig. He said he could demo everything and salvage the veneers/doors/front frames and was warning about having another company do the demo - he was saying if someone else does it they need to be extra careful not to damage the faces because he would be reusing those. Literally, he'd be gutting the cabinets/shelving and updating with plywood then reusing the solid-wood faces to reattach so the kitchen maintains its original look. We'll worry about refinishing/painting for a later time.
For the demo part I'm thinking maybe we should buy or ask them to put up one of those safety tarps/zipper doors that you can tape up to seal off the area. That way when they remove everything its all contained within that area. Not sure if that's as big of a deal but hopefully I can get some feedback from the damage remediation company later.
I think the order were we're going to do stuff is:
10/13 (hopefully later today) - damage remediation/restoration company to come out and get an idea of what he's dealing with then quote for the clean-up
10/14 (all day) - contractor to demo and salvage veneers/faces/doors
10/14 (end of day) or 10/15 (first half of day) - damage remediation company handles clean-up
10/15 (last half of day) - pest control company comes out to inspect for entry points and may start with sealing areas off
But now that I think about it, it might be better to try to get a pest company out today or tomorrow to assess/inspect and seal off areas of concern.