How do I replace a 7' drop ceiling so it matches an 8' ceiling with 2 layers of drywall and popcorn texturing?
What is the thickness of that second layer of drywall in your great room?  Chances are it's very thin, which you could hide by simply fanning out your joint compound to make a "ramp" 1 1/2 to 2 feet wide where the kitchen meets the great room.  Nobody would ever be able to see the difference.  Another option is to put a fake beam between the two rooms - basically a thin piece of wood trim that looks like a fancy support beam partially buried in the ceiling.  Again, nobody would ever notice the difference in the ceiling heights between the two rooms.  

There is a VERY easy way to get rid of the popcorn ceiling.  Get a paint roller with a fairly thick roller sleeve and put it on a long handle.  Dip the roller into a bucket of water, and then "paint" the popcorn ceiling with the water.  Use a bit of pressure to actually get the water into the popcorn, but don't overdo it and soak your drywall underneath.  Let that soak in for a minute or two, and then the popcorn will come right off.  Every time I paint a popcorn ceiling, half the popcorn wants to fall off with the roller, so I tried simply rolling it with water when I wanted to remove the popcorn one time, and it worked great.