I don't think that folding bead is the solution you are looking for. I don't mean this as an authoritative pronouncement, but rather as my impression from reading tire reviews over the years. The impression I have always had was this: Wire bead tires use steel wire for the bead. Folding tires use Kevlar fiber which is plastic. Kevlar stretches more over a long time when subjected to stress than steel does. For safety then you have to start with a tighter bead on a folding tire so it will still hold after it stretches. When folding bead tires were first introduced, they were almost impossible to mount. Folks who were used to looser steel beaded tires complained bitterly. I can't say why the LBS mentioned above won't mount wire bead tires on carbon clinchers, but I have to assume that these days wire beads are always looser than Kevlar beads, even after long use i.e Kevlar tires still come too tight but don't stretch as much as they used to. With the fear of the clincher rim softening from braking heat, one would want the tightest tire possible. At first that is a folding tire. Maybe it still is down the road.