depends on your definition of "doing it right" - I prefer to think of right as "as quickly and accurately as possible with the tools at hand - and enjoy doing it"
A forstner bit is designed to make relatively deep smooth sided holes - it also happens to be able to cut on edges & weird angles. As you can see from Mauser98's post - it does work (though I would use a fence as well) I have used the method before as well, it does work. But the forstner method 'is' the hack. (fun fact, the forstner but was invented by a gunsmith!)
Using a router & suitable bit (a spiral upcut, being specifically designed for this) will give you a more accurate mortise with very little or no cleanup required:
(done with a 3hp variable speed router, 1/2" spiral upcut bit and several guides)
A router will require more experience (speeds/feeds/cutter selection) and setup but less time actually machining.
Also - small side note - drill press columns flex, there is a lot of force required to sink that forstner, the mortice is probably not straight. That matters exactly zero in this case (when you are going to clean it up with a chisel anyway) but when you need to do something deeper or more accurate. keep that in mind.