It's best to apply early. EDP is for when you know where you want to go and you are pretty sure you'll get in. For instance, TT had matriculating averages of 3.65/29 last year. Despite what their dated info on the web site says, if you don't have at least a 3.75/30 and good EC's/LOR's, they won't even consider you for EDP.
EDP is not a bad thing, but applying late is. It is a risk, but one I'm willing to take since Lubbock is where I want to move my family and finding out 5 months early is significant for us.