They can be a mixed blessing. On site visitors come to that park around closing and replace the general crowd. We have done both at all of the parks at different times of the year including May and June. Mornings are always a benefit but as you said your family will not get up to go. Evenings are longer but the downside is no fast passes so if you went to Epcot to hit Soarin at night the line could be just as long as during the day. Other rides or the countries are good to experience though.
If you can swing it I recommend doing MK in the morning just once. Even though this is an hour long it can make a huge difference. The reason is that MK starts to really fill up around 10:30. Why? Because of all of the families with small children take additonal time getting to the parks. Once they get to MK they either head to Tomorrow Land or Fantasy Land first.
If you are at the gates at 8 this gives you about 2.5 hours of lower crowds. Those families with older children/teenagers will hit the bigger rides such as the Mountains. You can complete Fantasy Land in this time and move to another Land at about the same time as everyone else getting there. To be honest we have done all of Fantasy Land in about 1.5 hours with 2 small kids and gone back and hit the other rides by 10:30 finished and then moved to Buzz.
For example you get there, ride Peter Pan, Small World, Dumbo (the slowest load time), Cinderella, see Mickey Phil., Snow White, Winnie the Pooh, Tea Cups, Indie Cars, then you could do Toon Town or head and get a FP for Buzz. At this point it is probably around 10 am. Do the Astro Orbiter, people mover, Space Mountain, Buzz and the Laugh Floor. Time: 11 - 12.
Take a break. At this point it would be good to rest for a bit and maybe eat something. Now you could do Toon Town then take the train over to Adventure Land and hit that. If your family has had enough go back to the resort to rest and either return or hit a park with EEMH.
Also if you are focusing on doing rides centered around Derek then EEMH work well. Not all parents are going to keep their kids at a park until midnight or 3 am. If they are night people instead of morning people stick to what works the best for you. If it came down to it, stay until 3 am let them sleep in the morning and you hit the pool to do your own resting. Maybe there is a book you have been wanting to read but just cannot find the time until now.