Pass data through Perch Forms from another subdomain running on Drupal

Right, I'm going to guess this is either not going to be possible or extremely difficult; however, I figured I'd just double check in case I'm mistaken.

Here's the situation. We have a brochure site running Perch while the shop is powered by Drupal Commerce. Both sites share the same design for the footer. That's not an issue, but what is is that in the footer there is a newsletter signup form.

Currently on the brochure site, the form is output to a CSV and the customer's marketing team uploads that to their email marketing software.

We could replicate that on the Drupal side, but then it means they have two CSV lists to maintain. Ideally, I'd like to see if it was possible to have the Drupal form feed through via the action to the Perch Form; this would enable them to maintain one list.

Obviously, the easiest solution would be to get their email marketing software to generate a form that we can drop into the footer. But at the moment, we're not even sure that's possible as they've gone with a slightly obscure provider.

Any ideas?