All the glue in the world wont help that issue. You need to have fades off the core. Gluing flat stock on flat stock is no good. Nothing but glue stops the flexing.
Always start with 3/4" belly stock, then add a 1" handle on top of that. By the time you tiller it out you will have a nice, long fade created and it will stop the handle flexing, which cause them to pop off.