I have a '96 Ford Ranger Super Cab that I finally put a hole in the roof some 3 years ago. Similar to the previous reply, I had to drop the headliner to run the cable to the center of the roof. A friend of mine who has experience in doing these installations also removed the driver side seat belt bolt on pilar to allow the headliner to drop far enough to gain access. Droping the headliner is fairly easy; just take your time. There are screws that hold the sun visors in place and you may have to carefully pry the plastic that goes from the roof to the windshield; I don't recall how we got that off though. You will probably have to remove the dome light(s) too.
One suggestion -- if you decided to cut a hole in the roof, place a small box or something under the roof to catch the metal shavings from the drilling.
I used the Diamond NR72BNMO antenna to clear the garage. This antenna required grounding at the base which forced the issue of drilling a hole. For local around town use, this was a good compromise. The antenna has no gain, but the ground plane on the roof has to help some. The NMO mount allows mounting a gain antenna for long trips. For your Explorer, you might be able to use the roof rack to mount to. The problem is how to run the cable inside w/o crushing it.
Getting the power through the firewall: Your Explorer should be very similar to the Ranger. Look in the driver side pilar where the door hinges are. I found one unused rubber plug that comes out by the driver's side kick panel. This proved to work very well. If your are interested in more detail about the power run and fuse block installation, write email@example.com