Well, at this point XLN's response was to delete everything related to XLN, and try again. No joy. I've tried
everything that everyone here has suggested except for abacab's suggestion above, because I have no idea how to change the DNS settings (I know virtually nothing about networking, not my thing), so I'm concerned that if I start messing around, I'll destroy something unintentionally.
I did notice a "Network Reset" option, but it had scary warnings about needing to possibly reinstall other networking software, such as VPN client software or virtual switches. Since I have no idea how to do that, I left it alone.
It's particularly frustrating that I can connect to every other site I've tried, download programs and updates from all other sites, etc. Only the XLN installer gives me this problem, which is even more bizarre because I've downloaded updates to the installer from their site, so obviously I can connect to their servers and download stuff.
If XLN can't help any further, then I guess it's time to give up and move on. Not sure what I'll do with older projects that had AD2 in them. This pretty much sucks.