Check with Grant. He has hatch seal that goes down to 1/16 inch, IIRC it is double-D, and the price he quoted me (a little while back) was better then anything suitable from McMaster-Carr.
Some foam weather stripping intended for home use seems to me to be open cell foam, better suited for draft prevention than a water tight seal; cheap crappy stuff.
Following are just some thoughts re: getting seals to stick to wood. Not a lot of practical experience, just the $.02 that I have gathered over the years.
First, the wood has to be sealed or painted. Don't expect the peel-n-stick stuff to stick to raw wood (forgive me if I have not given you enough credit to figure that one out for yourself, but there are many people out there watching with all different skill levels, and I like to try and help everyone, not just the OP'er). The rougher the surface the less contact between glue and wood. The more sanding dust and softer grains, the less integrity for the glue bond.
Second, don't stretch it too much while laying it down. This can put shear stress on the glue bond and will work against optimum adhesion, me thinks.
Third, don't be afraid to use supplemental glue (like rubber cement or contact adhesive) to get a better bond. 3M makes an automotive weather strip adhesive in black, but be careful, it can get messy.
Fourth, a few carefully placed staples to pin down critical areas (like corners) could be effective so long as they don't squash the seal enough to breach the "line" of the seal. 'P' or double-D shaped seal profiles are great for this because they provide an area for staples to go away from the sealing beads.
Hope this helps some.
