First thing first make sure you're getting the right thickness in your drywall, not all lathe and plaster thicknesses are the same. Use variations of 1/4,1/2 and 5/8...5/8 usually does it but don't be mistaken...you don't want to be left with a 1/4 shallow drywall that you're going to have to mud over...entirely.
Next, make sure the L&P is solid.
You've cut the L&P which means you compromised it's integrity, general rule is if you can pull it off with medium pressure with the hand (pulling) then it's gotta come off so keep pulling it off until you can't take any more off without the use of a pry, hammer, etc.
Obviously try to cut straight joints...no jagged corners
Then go with what Butch said...I haven't done the 3' mesh thing yet though...sounds like a good idea.
I do this far more often than I ever wish to, but it always comes out seamless. And yes you will use a buttload of mud
In the end try to stay away from having to do this but sometimes the situation calls for it...I ALWAYS prefer to tear the whole wall down and go fresh.