Well...my locally available favorite of late has been a locktight product for roof and flashing.. It is a great adhesive...and remains quite flexible ..and obviously an outside product...I have used it on plenty of things...recently on my hiking boots by timberline...many years old the sole was detached from the leather shoe... It has held the two together all winter... And they are water tight...it is black... But cleans up with thinner when it is fresh.. It does take a bit of time to set up.. Perhaps more than a day for full adhesion when the surfaces are air tight...porus surfaces are quicker as air gets down against the adhesive and promotes setting up...
Sounds great... The bird houses look like hobbit houses ..don't they...... OH?..this is available at Home Depot so it is easy to find..