My issues certainly seem to have some similarities with #72330. Incidentally, when running with -T it (my small example) stops immediately for me with:

Insecure dependency in open while running with -T switch at /usr/local
+/lib/perl/5.10.0/Term/ReadLine/Gnu.pm line 620.
END failed--call queue aborted.
 at /tmp/d.pl line 0
Config::DESTROY(/usr/lib/perl/5.10/Config.pm:62):
62:    sub DESTROY { }
IO::Handle::DESTROY(/usr/lib/perl/5.10/IO/Handle.pm:76):
76:    sub DESTROY {}
IO::Handle::DESTROY(/usr/lib/perl/5.10/IO/Handle.pm:76):
76:    sub DESTROY {}
[download]

but if I add PERLDB_OPTS="ReadLine=0" and change to -T instead of -t it works fine. Disabling ReadLine gets me further in my actual code also although it inevitably stops sooner than I'd like as some real tainted data is in use which escapes with -t.

I am thinking of trying HTTP::Lite instead as it does appears LWP::UserAgent is the start of my problems here and I hear HTTP::Lite is faster and I'm only doing simple gets.

Thanks for pointing out #72330, I'll keep an eye on it and if you want to come back to me when there is a fix - fine.