RE: Titebond III
I had been using Titebond II for a long time with good success as a general construction adhesive except I did not use it for firewalls as epoxy is likely a better choice.
Recently, I have been using Titebond III instead of Titebond II. I like it because it develops a fast tack, sands well and flows into joints and wood grain better than any aliphatic resin glue that I used previously. Produces very strong joints, but you need to eliminate any "daylight" in joints since it does not bridge over gaps as well as the thicker versions of aliphatic resin glues.