well be careful about your glue choice. some aren’t rated very highly. for example I’m using epoxy for my floating book shelves.
OTOH, glues like titebond. do NOT and I repeat do NOT let the glue “freeze”
my dad has a friend that makes custom furniture.(expensive stuff too) she got this piece all glued together delivered and it suddenly fell apart. apparently after much investigating the glue had gotten too cold during shipment and it weakened it considerably. so a spiffy several grand project became kindling.
Probably either very gently treated (and tested) titebond or equivalent, or epoxy. Or (maybe) gap-filling CA. Not urethane, because you need good fit and pressure and it’s sometimes finicky about the wood. (I had a bunch of A-frames that I made with urethane for the water resistance just come apart.)
Also: lots of clamps. (I thought about vacuum, but there’s really not enough surface area, I think.)
I was able with something I built a while back to show the wifey just how many clamps can be involved in a project, so when I asked for them for Christmas etc. it all became clear.
I must say I’m very fortunate in that I explain to her what the tool is for and what it can do in the future. she’s quite accomodating. she has seen how my numerous tool expenses have manifested my ability to install the flooring.
