April 19 is the due date for your 90 day report. You can do it on line and pretty painless. You can do it afew days before and up to a few days after due date (I thingk 15 before and 7 days after, someone will correct me soon)
you will probably (almost definitely) need to speak to someone higher up the food chain in immigration in Phuket town office. Start with your wife making a phone call or send an email (in Thai) outlining your position. Phuket immigration even answer their Facebook messages. 🙏
As Ben mentioned, your wife will have a housebook from somewhere in Thailand. Probably the family home unless she owns property herself.
You will need a tm30 filed. That's for sure.
As for living on a yacht then that could cause you a problem. As you know, on your first extension, Thai immigration usually carry out a home visit. During this visit they try to talk to a neighbor and ask them about your household.
I use Phuket Immigration and they requested my wife's house book, house contract, landlords house book and housebook of the property that I was renting (that's a lot of housebooks)
As your situation is unique it may be a good idea for you and your wife to head down to Phuket immigration, explain your circumstances and see what they say. Good luck . Hope it works out smoothly for you.