This sounds like it could be my mom, although she's less persistent in terms of texts and stuff but she still tries to contact my wife from time to time with stupid stuff. I moved hundreds of miles away from my parents and stopped answering the phone when they call. Actually it's taken me a long time to be able to listen to voice mail because my mom would leave these long rambling passive aggressive voice mails. (Nowadays you can pick and choose which ones you listen to, which helps.)
I hope your husband has all the important documents, birth certificate, immunization records, social security card, etc, in his posession and not at the parents' house.
I would pick up mail one last time, maybe with a friend who the parents will have to behave themselves in front of because not family, and then contact each of the people who mailed the wrong address to get them to correct it.
Also, check your info at the credit bureaus and make sure they have the correct, new address. You can get that info for free once a year and you can challenge any info in it that's wrong. (Having said that, they can always put wrong info back and do.)
Don't flounce or tell them you're cutting off contact, just quietly do it. When you're ready, block their #s from your phones because they won't stop texting. If you give a forwarding address use a PO Box. It makes it harder for them to show up unannounced at your door.
It sounds like you are emotionally ready to cut off contact so good luck. In my case it was worth it. I haven't 100% cut off contact but contact is way less and I have no intentions of changing that. I am free to be my own person now. (In the case of my family there were issues way beyond just the trans thing, which is probably the case for your husband as well. Controlling people aren't just controlling about one thing.)
ps: you know about those mail forwarding cards at the Post office, right? Put one in for your each of your husband's current and former names with your parents addy and your current one. The reason is because those cards expire after so many months so even if you did it before, it's probably expired. Also, it only forwards 1st class mail. Bulk mail is usually of much less importance--magazines, solicitations, stuff like that, which you may not care to have forwarded anyway.