I say market yourself until you drop. If you are a high schooler in that second tier, then your decision on whether to go pro could very well depend on whether you go in the 6th or the 10th round. As for an individual team, perhaps they really want one guy with the makeup a kid has. It could be as simple as that team picking another kid because they had more exposure to the kid. If you cannot sneak in early (some scout saying - "Yea - we saw lots of this guy and his tools are documented - we didn't get to see the other kid nearly as much this spring"), then you may miss out altogether as the bonus gets whittled down and teams start thinking there could be signability issues.
What JOEMKTG outlined is pretty simple to execute and if you are in the draft discussion, you are going to be doing most it already. Why not bring some organization to the process and maybe increase your opportunities.