How about if you get a cheap prepaid mobile number and then port it to GV (after you've used it as a true mobile number for some SMS).
This will work if the number is with a real carrier when you register it for receiving SMS from the site. Once you port it to GV it won't work for other sites that have the same requirement. I think the OP is looking for a solution that will work for other websites in the future.
FYI, GV charges $20 for port-in.
Try TextNow. They'll give you a free phone number that can send and receive texts from their app. It shows up on carrier lookup sites as a landline and not a voip provider. The caveat is you need to send or receive a text once a week or so or they will take away the number and reassign it.