What is the best way to replace a large section of 3/4" plastered drywall?
Spend the time to clean the edge of the plaster so it is straight, this will save you time and make those top two inches that will be visible look nice.  I personally would use a heaver drywall (5/8) to closer match the original and use thinner shims (they sell a cardboard like shim for drywall).  Butt the new drywall up the cleaned up line and make sure to use a drywall tape to interface the old to the new.  If you don't, the two will surfaces will form cracks between them.  

You say the top two inches are the part that will show, but that will also be the hardest and most critical two inches to get right.  Drywall and plaster are two skills where experience makes huge difference in the quality of work.  It doesn't hurt to get an estimate from a couple of guys and compare that to the amount of time it will take you (plan on taking three times the amount of time as a pro)