another option would be to go to any place that sells boater's supplies and apply a penetrating epoxy to the wood.
If you're near a Lee Valley, buy one of these wood restoration kits:
Wood Restoration Kit - Lee Valley Tools
The two tall bottles have a liquid epoxy resin and liquid hardener in them. You mix the two together and paint that solution on your rotted wood. The liquid gets absorbed into the rotted wood, and as it cures and hardens it restores the strength of the wood.
One thing I like about this kit is that you can mix equal quantities of the thick pastes in the two short tubs to make a shape that you want to stick to something and it'll hold it's shape as it cures. (Like making an epoxy handle for a tea pot like they show on TV.)
And, you can also mix equal parts of the liquid, and equal parts of the paste, and then mix the liquid and paste together to make a compound that behaves very similarily to joint compound that you can spread with a putty knife into depressions or gouges in wood prior to priming and painting.
It's a very versatile kit.
PS: It's stupid providing only one of those tiny measuring cups with that kit. You can buy 100 of them for $3 at any medical supply store. Just ask for "prescription cups".