Can you take the Monorail from DTD to Tomorrowland for EE, or do you have to go in the main gate in the front of the park? We will be staying at the DLH so we can have EE each day that it is offered, but I really don't want to contend with the crowd and have to get there really early. Any advice?

No Guarantees, but yes, usually, the Monorail is up and running for Early Entry, the first train leaves the DtD right around the start of the EE hour, so you get to the park about 5 minutes after the hour, about the same time as the first folks that got into line at the main turnstiles entered the park to the Tomorrowland/Fantasyland area.

But to be honest, IMHO, the Main Entrance Plaza has many more turnstiles open and tends to move a lot smoother and quicker than the Monorail station at DtD which only has 2 turnstiles, and one or maybe two security CM's.

If you want to be there first, and/or quicker, the Main Entrance Plaza is the way to go.

In my experiences, the line for EE at the DTD monorail is much slower that the ones at the main gate. Since its only a single line you have to go thru the check points which has about two people working, and you have to go up the stairs or take the elevator if you have strollers or a wheelchair. I would suggest going to the main gate. I have tried both and the main gate was much easier and a little faster.