It really depends on which rides you don't want to miss. On a non-EMH morning, if you start in Tomorrowland you'll be able to get at least a couple walk on rides on Space Mountain and Buzz or start in Frontierland for easy ons at BTMRR and Splash. Haunted Mansion should still be walk on after you finish those, and you might have some luck over in Fantasyland with Ariel and It's a Small World. Lines for Peter Pan grow fast, but that's another option at rope drop, so you can see the new standby queue.
As an example, last year on a crowd level 9 day the first week of August at rope drop on a non-EMH day we did: Spaceranger spin, met Stitch, Space Mtn, Dumbo, met Ariel, FP SDMT, FP Peter Pan, It's a Small World, met Gaston, shopped, stopped for photopass, and a few other things all before an 11:00am lunch FP for Be Our Guest. We took our time, didn't hurry anywhere, just enjoyed our surroundings and still did quite a bit in two hours. Add in an extra hour for EMH and another extra hour for your goal time of noon, and you should have no problem getting a lot of things done.
I would look at a park map, figure out which rides are most important to you, make sure you know which rides are open during EMH, then adjust from there. Have fun and good luck!!