I made some test panel pieces some 15 years ago with laminated core materials: fir, plywood, balsa, foam (Divinycell and Inotan) – a very simple and unscientific test with 165 gr twill fiberglass on 5 mm core. My experience at that time was that fir was outstanding in strength/weight ratio. I did not have any WCR or Paulownia at the time.

With longitudinal balsa the test piece delaminated when stressed.
With foam and vertical-grained balsa I lost the longitudinal fiber strength of wood, which in a kayak is the most important quality (to handle tensile and compressive forces on the deck and bottom in waves), which meant that I had to use more or heavier fiberglass to compensate (saving a little in the low density core by adding a density ~1.8 fiberglass/epoxy). With double fiberglass layers it appeared as strong as the fir laminate, but was heavier.
With plywood strips I also lost a little strength – probably since half of the layers had the wrong fiber direction.

"Strength" here is some kind of subjectively defined mix of bending strength and resistance against delamination.

There is of course a lot more to it than this very simple tests indicate. It would be interesting to try thicker core, unidirectional weave, higher density foam, alternating foam and wood strips, foam and carbon/aramide, vacuum infusion to increase the cloth/matrix ratio etc. Furthermore bending is not a very relevant test for a kayak hull – if the strips really bend you probably have more serious problems than the hull material.

One of the lightest wood strip kayaks I have seen is a sea racer/surfski hybrid (625x44 cm) built by Roar Berge in Norway (4 mm Fir and WRC). It tipped the scale at 11,36 kg (25 lbs). I have yet to hear about an amateur built foam core kayak matching this...

Roar's surfski (alongside an older Nordic Kayaks surfski, from which the cockpit shape was taken):
http://www.thomassondesign.com/$2/file/newsimg/2012/news120727-2.jpg