PV,

Hi, my name is Marc-Alan Barnette. I have a business that helps guide writers through the process of writing, promoting etc. What you need to realize is that contest songs are judged against the others in the contest and might be great for that but a very different deal when they get to the real world of songwriting.
The first thing you should do is get some critiques on the song from independent sources before committing resources for a demo. If the company is offering to pay for the demo that is a pretty good first step. But even after the demo is done getting it pitched in a town like Nashville is never a given. This is a very competitive town and a LOT of people trying to do the same thing. If you have someone working the song that is a great deal and giving up half the song is very standard. That is the business half of the song.
For members of this and other threads I am involved with I often can do a quick evaluation on the song. If you want to contact me on my private e-mail I will do it for you no charge. You should just make sure you have the strongest thing you can before getting it into the market place.
Be happy to help if needed.

MAB