Titbond III is hella strong and great stuf, but, as mentioned, you need very well mated surfaces, and you have only a little time during glue up. I almost always do any glue up in stages with TB III, like if you have a handle, limb wedges, or power lamination to do, don't try to get all that AND the backing on.
I also have good success slapping a sizing coat of TB III on the laminations. I pour some glue into a cup and add a little water until it feels runny, but thick like house paint. I paint it on the surfaces, leave it a moment, and scrape off the excess with a popsicle stick. In a few minutes, while still tacky, I quickly load up one surface heavily with glue and lay them up. I think it really works well, but you have to watch out for some woods wanting to cup when you wet them.