I resolved this (from my perspective) by releasing and renewing the DHCP IP on my cable modem (and getting a new IP). Not sure what will happen to anyone picking up that old IP.
Original message stated something like 'connection refused - incorrect greeting'. Then after so many tries, the message changed to the 'timeout' message I complained about above (guessing it was because of some sort of anti-spam/hack blacklist from too many tries). I called support, went through the first level, was sort of coerced into getting premium support (though that person was competent and courteous). The next level said it was a known problem, that I would be added to the 'impacted' list, and to wait 24-48 hours for the resolution.
This morning (about 72 hours later) we were getting the 'connection refused' message again so I did the release/renew IP thing. I wish I'd thought of trying that 5 days ago.
Thanks for your attention!