Sorry -- the combination of GET and POST along with Net::SSH::Perl quite confused me.

You've already got quite a good answer from brother graff below, but essentially the problem is that you're trying to execute a secure, asynchronous process using an insecure, synchronous medium. It's just not a good fit.

Rather than focus on using Net::SSH, why not have a web application create a file in a certain location (perhaps based on the user's values in a form that you have them fill out), and have a cron job watch for the arrival of that file. When the file's arrival is noted, it can be moved (so it's not executed twice) and then used to execute a process, with the output data left in some suitable destination directory.

You could even send E-Mail to the submitter when the process is complete, or if this is part of a larger web application, flag the user that their job is done.