The construction adhesives will be the most affordable option for securing the wood to the shell. However if you do need a lot of strength you can thicken epoxy and it will easily take care of the issue of filling any irregular gaps.
You can thicken epoxy and use that as a glue for attaching wood to the shell. That is how I normally attach my wood blocking in the shell. But we normally have epoxy on hand and buy it in larger sizes and dispense it with a pump. Not something most people have on hand in their workshop spaces so you won't see a lot of forum members suggesting this method of attaching wood blocking to the shell.
I typically use the wood flour as my thickners as it is a very affordable filler although heavier than micro balloons which also make a good thickner. When using it on a vertical surface make the mixture thick enough that it does not readily fall
off your stir stick, cookie dough stiff
You can start with a thick version of epoxy resin if you wish although I typically don't since I use the same large container of resin for other projects where I don't want thick resin. I choose my hardener type according to if I need a fast cure, medium or slow. Part of the choice is to do with the weather, in hot weather I gravitate towards the slow cure. I do mix up smaller volumes of it as the mass of material generates its own heat which will accelerate the cure time.
A hot glue gun is handy for tacking the wood in place while the epoxy mix cures. Just run some along the outside edges here and there. The goal of the hot glue is just that it is a temporary way of clamping the board in position otherwise gravity takes over and slipping can happen. Overhead work requires bracing it from underneath.