To start with your last question first: This should take you less than three hours. Even going really slowly or making the wrong choices you will be done in plenty of time for a relatively early lunch.
That being said, I have some suggestions (at least one of which will go against popular wisdom)
First, I think the last two attractions on this list you should be Its a Small World, followed by Mickey's Philharmagic. Yes, you are going to walk past these attractions to get to Haunted Mansion, but you are also going to walk past them (or could choose to) to get from Haunted Mansion to the exit. IASW and Mickey's Philharmagic are both longer attractions (14 and 12 minutes) together (ride + wait + walking) these two attractions will take just shy of 40 minutes. Slotting that 40 minutes prior to Haunted Mansion allows the line at HM to grow while you are riding attractions whose lines will stay pretty steady until lunch time.
Second, I don't agree that you should do Peter Pan first. Every one is correct that by doing it first you will the shortest wait at Peter Pan, but while you sit and wait in line at Peter Pan, the lines for all of the other rides will grow. You should do Pooh first. if you go to Pooh first the wait will be under 5 minutes, then when you move on to PP it will be about 20 minutes of a wait there. If you go to PP first (unless you are jostling for position and fighting the crowds at the front of rope drop) the wait will still be close to 20 minutes for PP, but by the time you have waited for and ridden PP the line for Pooh will be around 10 to 15 minutes.
I might even push PP back even later and do it on my way to HM, getting the the other five fantasy land rides in during that first hour, but that is a little riskier.
Most people seem to think the best touring strategy is to take the longest line they might wait in and make it as short as possible by riding that ride first. This does indeed work in decreasing that one line, but often, while they wait to ride that single ride, all of the other lines increase. Sometimes they could have ridden four or more rides in a relatively empty park with no waits instead of that one ride. Those four rides might end up each having a wait of 20-40 minutes later, that saving an 40-60 minutes in that one line might mean adding 80-160 in other lines, costing up to an hour of touring time.
Of course, your situation is no where near as extreme as that. My way might (or might not) save you 10-20 minutes, and even doing it the worst way I could come up with would still mean you were done around 11:45 (instead of 11:00.)
EMH combined with a slow park day (due to the
MNSSHP that night) should lead to a nice relaxing morning. Don't worry about it too much.
