Dave hit on exactly what I was going to say. Titebond is plenty strong and I have used it in a lot of wet applications. But to get good joint you need a good mating surface, meaning that you would need to trim each frame to match the angle of the stringer and fit tightly. Then you need to be able to clamp it tight. That is very important to getting a good glue joint. That is why I lash mine together and that is what I recommend. But if you going to glue them I would stick with epoxy and perhap the P&L, I have never used it so I will defer to others on that.

Here is my video on lashing.
http://kudzucraft.kudzupatch.com/video/lashing.php