Woohoo! It works now :-) After digging this old problem out of the dead projects folder, I couldn't leave it alone. It seems that Crypt::SSLeay uses HTTPS_PROXY_USERNAME while LWP uses HTTP_PROXY_USER. In my testing, the HTTPS_PROXY env setting still needs to be deleted then set again. Changing the env proxy block of my code to this works now:

my $https_proxy=$ENV{HTTPS_PROXY};
delete $ENV{HTTPS_PROXY} if ($https_proxy);
$ua->env_proxy;
$ENV{HTTPS_PROXY}=$https_proxy if ($https_proxy);
$ENV{HTTPS_PROXY_USERNAME}=$ENV{HTTP_PROXY_USER};
$ENV{HTTPS_PROXY_PASSWORD}=$ENV{HTTP_PROXY_PASS};
[download]

Yay! Now I have to go write the rest of what I'd set out to do in the first place. Another dead project lives again!