Thanks. Looks like I'm at 6.02 so I'll go in that direction. It's a Windows box so I'll be using ppm to grab it. I'll update outcome whether good or bad.
It looks like the problem was actually certificate verfication. I'm guessing that the earlier release we upgraded away from defaulted the ssl_opts key verify_hostname to FALSE. LWP 6.02 defaults to TRUE. Everything is working fine now thanks to the hint on the debug output.