What about a computer with a cellular card, or a phone tethered to a computer with a USB cable?

Though I don't know anything about software for that configuration, I'm sure it must exist, or, you could figure out the API of the cellular card and roll your own. At my old job, I had all the necessary resources at my fingertips to write the software.

Here's a youtube video showing a piece of software sending a mass SMS from a computer via a tethered phone. From the looks of the software it looks like it'll support multiple tethered phones.

https://www.youtube.com/watch?v=rFbXjLvcjZg

Don't know if that particular software is any good, I'm just linking it as a proof of concept that this configuration can work and does have some kind of software support out there.