In soccer, I do not feel that a regulation size field, with a good surface, gives much of an advantage. Now, if the field is short, narrow or has a bad surface, it can totally serve as a plus to the home team. CCS has a very nice field and I think lost in the state tourney there last year.
Another solution, would be at least play A/AA at GPS and Division II at CCS.
What I don't understand, is why is it in Chattanooga? It would seem that Nashville would be a better choice for the entire state. Vanderbilt, Belmont, David Lipscomb, and Trevecca, to name a few, have incredible fields.