Hello, and welcome!
The TSA understands that many people misplace or lose their driver's licenses (and, as you already know, an expired license is not valid), so they have alternative forms of ID you can show at security screening. Here is a list:
The notary guy, trying to help you out, is very nice, but I don't know if that would be acceptable. There's no reason not to try that, but, in the case that you don't have any of the alternate forms of ID to show, don't worry, because the TSA can access multiple publicly available databases with information to confirm your identity.
Bring the expired driver's license with you, so they have that information, and you should not have a problem getting on your plane. However, I would leave at least an hour of extra time at the airport, since you will have to be screened in a different way and it might take longer.
I hope all will work out well and wish you safe travel!
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