I have read a number of threads on a number of sites and am still unable to make this work.
I have a client machine (OSX) with OpenSSL 0.9.8r running perl 5.12.4, w
Instead of using Net::SSL which does not provide much host verification (and no SNI) you can use Net::SSLGlue::LWP. This monkey-patches LWP so that https_proxy can be used with the default SSL backend IO::Socket::SSL:
use Net::SSLGlue::LWP; # do this first
use LWP::Simple;
... continue with normal LWP stuff..