Here's what you do:
take the DAT as soon as humanly possible. I don't quite uderstand how you can't get rec letters sooner. Do you not have a predental committee at your school, and why can't you ask proffs in classes you already had (you must have had 3 years previously, right??). But, unless you make 21 up and have a 3.7 up GPA, or something outlandish (like ex-astronaut or secretary of Defense), I would be concerned. Oh yea, and apply to a ton of schools, every bite counts, right?
So, there is something remotely resembling a constructive advice. Invites to most schools have already begun, and the rest will join in about 2 weeks.