I used Morning EMH on my past trip the first week of December for DHS, AK, and EPCOT (in that order). I felt i worked out pretty well for me but bear in mind the DHS & EPCOT EMH's were 7:00AM and the EPCOT day was also the day Rise of the Resistance debuted. So EPCOT was relatively dead, until mid-morning as I think a lot of people were coming in from DHS.
Some things that worked for me (but YMMV because of the different times, time of year, and circumstances):
-I had an FP for SDD so opted not to follow the crowd to either GE or TSL. Sunset Blvd was practically dead and I think there were maybe 20-30 people heading to RnRC and/or ToT. TSMM was my next ride and practically a walk on. ASwS was about a 15-20 min wait.
-If you use AK EMH and you're on-site, go to the left. That is where they check-in on-site guests for EMH. Also note, if you are not at the very front of the tapstiles, the crowd builds really fast for FoP. As our line got held up in the tapstiles I saw any early advantage slipping away & since I had an FP for later in the day, opted not to use EMH for FoP (wait time when we got to pandora was over an hour). Walked onto NRJ instead and did other attractions after. Got to KJS just as the park opened. Posted a 40min wait but line moved fairly continuously so was about maybe 20min tops.
-EPCOT - The world is pretty much your oyster for EMH choices. I would save Soarin' for when the park is just about to open to everyone else. Use EMH for whichever other ride (FEA or TT, assuming you have interest in either) you don't have an FP for. I actually got through the gates just a few minutes after EMH open due to a relatively late start, but the park was still pretty dead. I got through my FP's really quickly as I was able to move both my second and third and finished everything with any major lines by 10:30 (Anna & Elsa had a 50 min posted wait and I think we only waited half an hour).
As others have said, make sure to get there before EMH, at least an hour early. Particularly for DHS & AK. EPCOT I think you technically have a little more leeway but security there right now is a pain and can delay your entry. I lucked out getting into the park just as it opened, but as mentioned that was also the day RotR debuted. I think Morning EMH is actually a good strategy as long as you can get up & arrive early enough. No experience with Morning MK EMH or any evening EMH.