I suspect it could be the same old issue, which comes up from time to time...  I.e., in order to use a proxy with HTTPS, you have to set the environment variables

$ENV{HTTPS_PROXY}          = 'http://proxy.domain.com:8080';
$ENV{HTTPS_PROXY_USERNAME} = 'nt_user';
$ENV{HTTPS_PROXY_PASSWORD} = 'nt_pwd';
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instead of telling the LWP::UserAgent via

$ua->proxy(['https'], ... );
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Those env variables are being interpreted by Crypt::SSLeay (used under the hood for HTTPS connections), which should then handle things correctly.  Good luck.