What should I do to get into a GS residency? You should have a pulse.
I'm kidding. DOs still have some trouble obtaining a spot even though overall applications are down. It's sad that you could have better grades, more research and better USMLE scores but may be competing with a much less qualified applicant simply due to the letters after your name. But that's an entirely different topic.
GS apps are down which is great for you! Of course the things you need to match include good grades, good USMLE scores, and possibly research if you had time to do any. Anything to set your application apart. No surprises here.
A rotation at an allopathic program with a letter of rec from that chairman would be of great benefit to you. Not only do you have a letter from an M.D. but you possibly could improve you chances of matching at that program if you shined during your sub-I. I recommend you look at all types of programs. More well known academic programs are less likely to accept a D.O. Sucks but that's the way it goes.
A good place to research programs is FREIDA as well as scutwork.com.
Prelim positions are for one year and they are extremely easy to obtain. If you don't match a categorical position, you will have no problem getting a prelim spot. These spots can be a stepping stone into either a PGY-2 spot or making you competitive for a categorical position starting over with another PGY-1 year (which would suck but at least you are obtaining your goal). Anecdote: I have a D.O. friend who did a total of three intern years before matching into a categorical spot. Luckily, the program was at least nice enough to make him a PGY-2.
It's always better to try and match straight into a categorical position if you can.