You have a decent chance of getting in, and your MCAT will largely determine where you may be competitive. Your research experience will be around (slightly above) average for applicants, which is a good thing. It really behooves you to do the absolute best you can on the MCAT (36+), in which case you will almost certainly have many options. Shoot for your absolute best, and the 'bottom' where you should feel comfortable is perhaps at 32 or so.
I do not think the HES is very important. The MCAT is really what you should be focused on and will make or break you.
Note that if you want to matriculate right after this 2 year research gig, then you will need to apply during the next cycle (starting June 2013). This means you will take the MCAT between now and then, write your personal statement, MD/PhD essay, and research essay, and get all of your Rec letters completed for your application to be submitted by mid-July at the latest.
Best of luck.