furry, I'm not recruiting right now so you might be right, but I'm fairly certain that there is a bigger discrepancy then that in money for CV's between 20 and 500 miles (more like $800 to $1,300, perhaps).
schro, it does sound like you'd be able to sign that kid. Now you have to refer back to the second question -- is he really worth battling for? Regardless of whether he had the time to actually drop through DII, he's a kid who's readily available to DIII programs, so the odds are still pretty good that you can do better.
On an unrelated note, if recruiting just started, there's really no reliable way you should be able to say that you have $5K allocated for this kid. There's just no real way to know what it might take for other recruits, and trying to guess is a fool's errand. You might easily sign a kid for $1K, or you might have to battle for the same kid and he could cost you 10x that. There's simply no way to chart that in advance that's even semi-reliable.