If the provider offers Curl commands as "documentation", you can convert these Curl commands to Perl code using HTTP::Request::FromCurl resp. curl2lwp.

I haven't gotten around to writing generators for other HTTP backends. If performance is of interest to you, maybe HIJK is a bare-bones enough client.

Alternatively, maybe take a look at using their command line tool from within Perl in parallel so you can handle more files at the same time. Also, maybe the command line tool can handle multiple files/requests in one go, or maybe you can modify the tool to do so.