The problem with this is that it's likely coming from an email server instead of an actual phone.
I had a similar situation, but they were benevolent circumstances. I had a difficult time working at home to know when to stop working at maybe eat. My friend set up a shell script that would run at 5pm EST that would SMS me to remind me to grab some dinner and maybe stop working if I was at a good stopping point. Each time the SMS arrived, it would be an incremented number. He had also previously set it up to remind me at lunch to eat lunch and to take cigarette breaks throughout the day. Those numbers were different even from each other and incremented on their own.
So say you find the header info and find out the email address of the sender. Great. Well, it's ridiculously easy to register a new email address, or even spoof one with an open mail relay. This can all be scripted and automated.