Thanks, Tony, Laurent, and Steve for the continued input and ideas.
Laurent, I may be over-thinking it, but I'm going to keep thinking about it until I come up with a solution I like enough to build.
A crucial factor in this is that my FB is elevated significantly above the top. This makes a BIG difference. I've made one guitar with a floating FB where there is just a small gap between the top and the underside of the FB (at first glance, you wouldn't even notice that the FB isn't glued to the top in the usual manner). On that guitar, there is no issue with the heel flexing (it does have a hardwood dowel in it - 3/4", if I remember right). Once you raise the level of the FB, though, the leverage exerted by the string tension goes way up, and the bending force on the upper part of the heel is much, much higher. My experience suggests to me that the heel needs to be stiffened A LOT to make this work. I seriously doubt a couple of 1/4" CF tubes or 1/8" CF rods, for example, would do it. Tony's idea might work. A substantial steel rod or tube, or a large CF tube, probably would work (though I don't know if any of these have been proven on a substantially elevated FB like mine), but there are construction and/or weight issues with each of those options that I'm less than completely excited about - not that I've scratched any of these off my list of possibilities under consideration, just that I'm not diving into building any of them until I've given more consideration to other options and exhausted my ability to brainstorm new ideas.
Here's my other idea, spawned by Jeff's reminder about efficiency. If the outer surfaces of the heel, where the tension and compression forces are concentrated, are stiffened, then the material used to stiffen them wouldn't have to be as stiff as what you need to use to stiffen the heel from the inside, because it would be working in a much more efficient way. In other words, it could, perhaps, be wood, rather than steel, CF, or what have you. Wood is pretty and can be carved, unlike CF or steel, so I can imagine ways of using wood that would be visible on the outside of the heel. For example, I could make a spline out of ebony (not the stiffest wood in the world, but pretty dang stiff), grain running up and down the heel (all the way up to the bottom of the FB), say 3/4" thick, that goes
all the way through the heel, front to back (imagine my walnut spline; eliminate the part that extends to form a tenon, and extend it in the opposite direction right out through the heel). Once completed, it would show on the outside of the heel as a vertical black stripe that terminates where the curve of the heel straightens out into the shaft, with a semi-circular end. I think that would be quite handsome, actually. Moreover, I suspect it would be stiff enough, because the compression-and-tension-resistant long grain of this very stiff wood would be working at the two outer surfaces of the heel (on the inside and outside of the bending forces) as well as all the way through.
This would be a bit complicated to construct, but not too bad, I don't think. I'd probably make the neck extension a separate piece, like is typically done on archtop guitars, to simplify construction. I wouldn't have to deal with drilling, threading, routing, cutting, etc, steel or CF - a big plus, in my mind. The ebony would add some weight to the heel, but, with a butt joint and a thin neck block, and no heavy steel (except for the bolts and inserts) or CF, I don't think that would be too bad, either.
Have I explained this clearly? Any comments, criticisms, skepticisms, holes to shoot through my reasoning?
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