My experience is EXACTLY that of Mr. Andrew R. Stewart. On the road bike that I liked, I was "balanced" in such a way that I could lean forward over the bars with virtually NO weight on my arms & wrists. Or, as I said before, I could pedal with my hands an inch above the bars with no strain at all. Going to the levers or drops produced an "unloading" of my back.
Yes, I DO want drop bars for their variety of hand positions. I would prefer a recumbent, but WAF prevents me from considering one. Therefore a "road bike" it will be for me. Until my weight recedes some more, I'm reluctant to consider anything with carbon fiber (I started this year at 285, but now am 260). My goal for 2015 is to hit 230, where I plan to stay.
Frame geometry will be critical in finding that "balance" that I seek, but as Mr. Stewart mentions, it is elusive (and even the bike shop kids don't seem to have a clue). For now, "go ride a bunch of bikes until you find one that fits" may be the best recommendation that I've heard. I certainly don't know enough about frame geometry to even consider the expense of a custom frame without knowing how it would fit. Based on my (bad) experiences with the past few bikes (all of which had compact geometry), I was blaming the frames, but it may have just been a matter of fit, instead.
My pants inseam is 32" (actually, closer to 31, but most pants are only available in 30 - too short - or 32 - slightly long). My shirt sleeve length is 36.5 inches (again 36 is slightly short, but 37 is slightly long). Suit size is typically 50L (I have wide shoulders). I am between 6'2" and 6'3" tall. I know these aren't precise enough for bike fitting, but they're the best I have for now.
FarHorizon
Here's the Kona Unit as I bought it (profoundly uncomfortable):
Here's the Kona after my first attempt at modification (still uncomfortable):
Here's where I gave up & tried to make it a cruiser (still uncomfortable):