I haven't seen this before. I would guess that the issue isn't with the monitor configuration or the BIG-IP, but with either an intermediate device which decrypts the SSL or the web server itself. Your plan for testing on a server you control is a good one. I expect you'll not see the issue there.
You can also enable debug on the monitoring daemon, bigd, to see the request and response send/received for the monitoring. You can enable debug from the command line using 'b db bigd.debug enable' and disable it using 'b db bigd.debug disable' . It can create a large amount of output (logged to /var/log/bigd.debug) so don't leave the debug enabled for longer than necessary.
Aaron
Altostratus
