Sorry I'm late in getting back to you, but tomorrow is the opening of our gun season and I had to work late in order to get the next two weeks off for processing.
Anyway, we get some deer like you described every year. What we do is to use baking soda to remove the odor. If it's already quartered or de-boned then dissolve 1# of baking soda in a sink full of cold water (five gallons or more). Put the quarters or meat in the solution and let them soak 1/2 - 1 hour stirring occasionally. Drain and rinse with cold water, you can then dry it by placing on paper towels. The meat may look lighter than when you started but most of the odor should be gone.
When processing a gut shot deer I always recommend using seasonings and marinades with the steaks and roasts, and making seasoned sausage, meatloaf, etc either the trim.
You should not have any issues as far as getting sick, as long as the temperatures were not exceedingly high the night you waited.
Dave