But we are trying to import into a local WP install, on the server.
Right, I'm saying, as an intermediate step, to import it into somewhere where you actually can make it import, then export it from there as a WordPress export, and THEN import it onto your other site. See?
We're running PHP 5.2.6 and we do have OpenSSL installed as well.
Clearly, you don't. Or, at least, PHP does not recognize that you do. The only way you can get that message is when your PHP instance doesn't support outgoing SSL connections. That's a PHP error. Google for the text of that error and you'll see what I mean.
Blogger/Google only allows code like the WordPress importer to access blogger blogs over SSL. So your PHP instance must support outgoing SSL. You have to reconfigure PHP to be able to do that sort of thing.