I typically resolve this sort of situation with a ssh proxy such as ssh -f user@123.456.789.012 -L 9999:127.0.0.1:8983 -N
Then I can access the solr GUI from localhost:9999 on my machine, and all the traffic is secured by SSH. Pick your local port (9999 here) as desired of course. Sometimes I have to do two layers of this if there is only a single machine accepting SSH for the remote network. Of course this requires that the client be able to give you SSH shell access.
