"Rather than the 3 handles, are there any drill presses out there that use a wheel to advance the head? =A0Am I missing major drawbacks? Puckdropper"
I just saw an article (did not save it/bookmark it - sorry) about a fellow who exchanged the three handles for a large Pulley (maybe ten inches or so) and fixed a cord to it and the cord to a couple of pulleys mounted to the wall behind the drill press tying it off at a paddle affair mounted on the floor.
He could, then, hold the work with both hands - should the need or desire arise - and use the paddle affair on the floor to drill the hole(s).
I met a fellow in Florida a few years back who had modified his drill press so that the spindle could be made to "oscillate" up and down while turning. This feature allowed him to attach a drum sander to the press to finish work.
Back to the first "guy," guys, it would seem that, where the pulley large enough, it would serve as implied by the OP - although a smaller pulley would be better for the foot-operated approach as the limited range of the foot paddle (6" or so, as I recall) would significantly reduce the spindle travel were the wheel attached thereto very large.
I wonder if one of those automotive steering wheel replacements (J.C. Whitney) wouldn't make a real comfy drill press wheel at a reasonable price. Years ago they sold some rather small replacement wheels - maybe ten inches in diameter. The spokes on some of these are set at an angle that should provide the requisite clearance.