getting a big hole to maintain desired alignment when you drill is a challenge. Augers tend to make their own path in some woods. Shipwright bits of good quality can be controlled somewhat easier in a heavy weight drill. Cutting a 2" hole for your mortise followed by a square corner chisel may save a lil time but you are crowding the usual max dimension of the mortise.
In really heavy stock a set of clamps, a metal frame and a large electromagnet jig holding the drill (kinda like a portable drill press) has been used to keep the holes straight when boring thru for pegs. You may find a picture of this on the Franklin Farm project file.
Whatever keeps you in control is what works best.