I'd given BJ the wrong ip for the server to connect to Solr, so I wasn't able to get anything to work. That's now fixed, and I'm able to issue queries from the server using GET and get useful responses as expected. I still have a lot of work to do on the XQuery library for eXist to do this, though; it complains about the URL I'm contacting being invalid -- it has complicated query-string components that need escaping in various ways, and I haven't yet figured out the right combinations and escape mechanisms to get it working. Slow but steady progress.