I’ve also never heard of or received a signed invoice.
Regardless - If I were in your situation I guess I would just sign a new invoice, and perhaps mark it as a “copy”. Obviously you want to get paid - so if issuing a new invoice (or a copy of an old one) is what it takes… then so be it.
Ultimately - if you’re doing any sort of design work involving invoices I would suggest investing in one of the many accounting software solutions. They are easy to use, inexpensive, and most importantly allow you to present and track your invoices in a professional manner. In the long run it will save you tons of time.