MadTS:
You may want to research epoxy glues. I use West Marine, and I believe Shipwright does, as well. These are two-part adhesives – a bit more involved, have extended ‘open’ time and are water-impervious. I’m not sure that TB3 is intended for in-water or saturation situations.
I’ve completed several external furniture pieces – all mortise & tenon, and have never had a joint fail.
MJCD