Peter, I have used TBII and TBIII for hickory and boo backed bows with all sorts of belly woods and 3 tri-lam bows. Either glue is strong enough for bow building. TBIII has a shorter working time and that can be problem in some applications. With all TB glues you want flat smooth glue surfaces...no grooving or roughing up(as per the TB folks) Also the glue will let go at 150deg(F). This can be good or bad! I wanted to remove a backing strip from a failed belly so I called the TB folks And I was told to heat it to 150deg, work a blade between the lams and work them apart...and it worked like a champ. Placing a bow, glued with TB glue, in the direct sun or in a hot car could be a problem although I have never had a glue joint come apart accidentally.
The best part I like about TB glues is they are readily available, cheap, clean up with water and no fumes. Pat