If quartersawn beech is too hard to find, mesquite works quite well for
some type of planes.  Mesquite is very stable and hard.  It can also be
brittle.  Don't believe people who say you can't work it with hand tools.

I still use this jack plane I made from mesquite:
http://www.mwells.org/woodworking/planemaking/philly-style-jack-
plane">http://www.mwells.org/woodworking/planemaking/philly-style-jack-plane

A friend from the local woodworking club, Brandon Berdoll, runs a sawmill
near Austin,TX.  He specializes in huge slabs,  but he also sells small
pieces of mesquite that would work very well for laminated planes.
http://berdollsawmill.com/

Mark