You should just determine which carrier hosts the phone number and then go get a job there as a customer service agent or store employee. You'll get full permissions to change accounts, so you'll be able to make the change, fix your gmail, then change it back.

You probably risk some legal fallout though, so be cautious.

I recall reading that twitter was getting "scammed" because there were some phone services that cost money to receive texts (and possibly some of it was being passed on to the customer of said phone service) and they were getting spammed with phone verifications to get the payouts. I guess when twitter extorts your phone number out of you under false security pretenses and then uses it for advertising that's legit but if some one tries to a get a cut for themselves it's a big problem.

It occurs to me this "force you to send the sms" might be a way to avoid exactly this sort of thing.

They used to do just that, though people could pay about $25-30 (in like, 2008 dollars! So that’s closer to $47 today) for ‘unlimited text plans’.

I know you mean charge just these bulk senders, but if they didn’t charge consumers a similar rate too, whoever wants to spam SMS can just set up farms of consumer SIMs and dump them onto the network that way. In fact, they already do this.