Since there was no obvious scam, I've been wondering what the motivation for these was, and actually started worrying about whether someone might be trying to compromise my phone via some yet-undisclosed SMS exploit - why else would there be a systematic effort to get me to spend time exchanging a few pointless messages around the "wrong number" pretext that otherwise went nowhere?
I tried calling the senders by phone and found they were all Google Voice numbers, which eliminated the possibility that some actual rich guy had innocuously ended up with a number similar to mine.
I asked a few friends and no one else was experiencing the same thing. Glad to hear it's not just me.