In joints its all to do with area and having no movement on any right angle joint. Bonds with large surface areas are more difficult to break.
Titebond II has amazing strength when used on materials its designed for and remember foam is not one of those listed.
Lets take it as read that you are a good woodworker so your joints before the brads would be tight in the first place and no doubt the chair design is not all right angle joints in the same oriontation. PVA will not fill a hole, well it does but it will have no strength. It works on a tight joint where the PVA bond just helps the mechanical joint and stops the movement.
Your guitars are wood to wood bond and thats different as its what PVA is for and no doubt they will have really tight joints over a large area
As to the longbows, again thats wood to wood so the joint is stronger than the wood and no doubt the wood was clamped tightly together.
Clamping the parts together make the joints stronger and we cant clamp the cloth as far as i can see.
I think this explains:
http://www.titebond.com/Download/pdf/HowStrongisYourGlue_FWW.pdf
And this
http://www.titebond.com/download/pdf/ww/PremiumIITB.pdf is about Titebond II and it clearly states under limitations "Not for structural or load bearing applications" as does all PVA glues
Titebond II / cloth should not work as the foam is not porous but it seems to work, but I think thats just because its bond is over such a large area that the load is spread so it just does not move.
By the way we should refer to it as TiteBond II as T2 is a polyurethane glue made by Sika. (Which may well work better.....)
Maybe we should have a post with links to product spec sheets so people dont get mixed up.
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As to my dear old dad well he cant remember what dod of the week it is, what he had for lunch or that i called him 10 minutes ago but he can remember the war and all his working life and i am sure he would have made an amazing TD