Mark I tend to shy away from offering advice on something like this because you are going to get a ton of opinions on something like this and sometimes it gets confusing trying to sort it all out but I am going to go out on a limb here and just share some personal experience I have accumulated over a period of years using different glues. Some years ago I had the pleasure of spending a few days with Tom Morris in his shop at his home in Anniston, Alabama for the purpose of learning to build better. I thought I was a pretty good builder until I watched Tom build and I learned very quickly I was a novice compared to him. In a period of a few days I probably learned more about how to build a model than I had learned on my own by trial and error over a lot of years.
One thing I noticed was that he used Elmers white glue almost exclusively in building a model. But, and this is extremely important, he had a very specific way he applied the glue. He used either a two or three ounce plastic bottle that utilized a luer lock 14 guage needle on the top from which he dispensed the glue. What was more important was how he APPLIED the glue to the part or parts that were to be joined. He applied the glue in dots about 1/2" apart. He never lathered the glue on and smeared it around on the part to coat the part. For example: You are wanting to apply the leading edge sheeting over the front of the ribs back to and including the wing spar where the cap strips will meet the back edge of the sheeting. The way he did it was to place a series of dots of glue on top of the rib all the way back to the spar. Then, if you were using a piece of 1/4 or 1/2" square stock rotated to the diamond shape for the leading edge of a fish mouth rib, you put a line of dots of the glue along the edge of the leading edge piece where the fishmouth of the rib would capture the lading edge. Then you put a series of glue dots along the top of the spar. So in essence you have covered the front skeleton of the wing from the spar forward with the glue. You then could either pin the sheeting in place or weight it down or use a combination of both. He also glued the wing into the fuselage of his profile Cavalier with Elmers, not Epoxy. We even did an experiment where he glued the center sheeted section of a wing into a profile fuselage and challenged me to pull it out after it dried. I managed to get the wing out and broke the fuselage in half in doing so because the joint was so strong.
Randy is right about the water in white glue like Elmer's/Titebond and if you smear a ton of the stuff on the parts you are probably going to get a warp. I use white glue in building my models almost exclusively but you have to know how much to use in an application and how to apply it (the glue bottle with the luer lock needle. I really do not like using CA unless I absolutely have to. It burns my eyes, the fumes are not pleasant and I hate what it does to my finger tips. In the few applications where I do not use white glue, I use West Systems Epoxy. Most of the profiles I build are two pieces of 1/4" laminated together. I have used both white glue, applied as I described above, and the West System Epoxy to join the pieces without warpage using both methods. Again, doing this with white glue, it is pretty time consuming to apply all of those dots of glue. It is faster using the epoxy because you can brush it on and then scrape most of it off. If I were laminating flaps, I would probably use the expoxy simply because they are long thin pieces and are more prone to warp because of their shape.
Clamping and weighting the pieces down is very important. I have a flat glass surface that I lay the parts on and I use bridge shims which are square steel plates that are about 3/8" thick and are heavy to apply the pressure. I have some that are 4" square and some that are 6" square and they work great for applying weight to the parts.
This post kind of grew as I typed but I guess the important point I was trying to make was the Elmers white glue is a great glue to use but use it in the right places and apply it as I have specified above.
I hope this helped...
Mike