I ended up solving the issue. In case anybody run across this in the future, here’s what it was:
I narrowed the issue down to the template itself by stripping out all of the markup on the page, which allowed the form to work as normal.
I then narrowed it down to the <form> tag that was causing the conflict. Essentially, the GravityForm generated <form> tag and the one I had in my template were clashing. I should have seen the double <form> tags, but missed it.
I’m all set now.