My face shape is similar to yours (and I have ridiculously thick hair too) and I can tell you 100% that shortening your sides will make your face look longer and leaner and that you should DO IT! I've had my hair mostly short for the past 20 years so I've had some time to try a LOT of different things, including doing a fauxhawk.
And to clear this up, a mohawk is shaved to skin on the sides and the spike is all one long length. A fauxhaux the sides are longer and jelled down, and the top is gelled into a point. That's the basics, anyway.