We did Xmas day at MK in 2004. We had breakfast in the castle with the princesses.
Xmas Day 2004 was a cold, wet, miserable affair, so when we arrived at the TTC at 7.20am it was still quietish (though filling up fast). The rain was pretty heavy early on, but let up to a drizzle by 8am. After breakfast, we managed to do a few rides but by 11am, the rain had let up and people were pouring in. It was PACKED. The parade route was 10 deep in some spots (with 2 hours to go!!) and as we left at noon, even more people were trying to get in- mega, mega, MEGA busy!!
So, if you ARE going to do it, get there EARLY (rope drop was at 8am at the bottom of Main St, so aim to get to the TTC for 7.30am). Dont expect to ride anything you havent Fast Passed after about 10.30 (earlier if the weather is good!). If you want to eat in the park, you will need to book as early as possible (100 days out if you are staying onsite). Personally, I would eat at Jiko later.
Yes, you would probably get into Epcot later. Its a huge park and I dont know if its ever reached capacity??!! Anyway, later on, folks with young kids (like us) tend to be back at our hotel / villa so you would probably be fine (though it will still be very very busy).
Have fun!