Large drywall patch: how to avoid bulging seams?
While the usual trick for super-flat butt joints is to set the gap between studs (see the first answer in Should drywall be hung horizontally or vertically? for an excellent description), it doesn't seem like your situation would work for this.

Sadly, the best advice is to get a 10 or 12" taping knife and feather, feather, feather. (I personally wouldn't try to taper the existing drywall, as the paper is an integral part of the structure, and shaving some of that off would undermine it.) 

This is personal preference, but I'd use mesh tape that's advertised as "ultra thin", such as FibaTape Perfect Finish. (Some say that paper tape is thinner, but if you compare rolls in the store, I think you'll find that this stuff is actually thinner than paper.)

When I started, I'd put way too much compound on, then have to sand a bunch of it off, then repeat. I'd now suggest lots of thin coats to avoid the curse of sanding and having drywall dust floating everywhere in your living space.