I had a similar concern last year, coming from an east coast state school that did not have a national reputation. I was able to get interviews at a number of top programs, and for me, my research background (multiple papers/posters) and letters from well-known surgeons (my research mentor, and 2 from away rotations) helped get my application selected for interviews as a non-rotator at competitive programs.

So for you, bottom line you should try to add to your research accomplishments and rotate well this summer. I don't know much about Midwest programs, but I don' think any of the ones you mentioned are crazy competitive (aside from Rush in Chicago). For Indiana, I do know they only interview people who rotate there or have personal ties to the state. If you are thinking Midwest, I think Iowa and WashU are among the best programs in the region and should garner consideration as well. I think you have a solid application already, and I think you should rotate where you want to match. Programs will take a student from any school if they like them. Just remember that when you come from an unknown school, you will be at a slight disadvantage, but it is not a deal breaker by any means. It absolutely wasn't for me.