One possibility is to use directional knitted "cloth". The orientation which might be most useful is the 0 degree/45 degree/45 degree "triaxial" cloth.Especially on the inside and with the 0 degree orientation across the grain.

I don't know if anyone makes this material in light enough grades to be useful for kayaks.

It's expensive.

I was impressed by the performance of the Kevlar inside/ glass outside layups.

: The results seem to compare with my experience with kayaks and marathon
: canoes. Damage is usually caused by hitting a rock, which causes a
: compressive force from the outside. The damage I always observe is a crack
: longitudinal with the boat and the grain of the strips, on the outside of
: the hull. The fiberglass on the inside of the hull almost never breaks,
: though it is in tension under this situation. This is consistent with the
: data which shows the samples with strip orientations at 90 degrees failed
: at lower loadings, with the failure on the side of compression. No rocket
: science here.

: Now the question is how can we reinforce this weakest orientation in a strip
: hull in a practical manner that doesn't add excessive weight?