WME and Linda,
Thanks for the insight. I will try this method - it makes sense. I'll also look into other glues. The Gorilla Glue had the longest, most narrow applicator, so I went with it because some of the gaps are small (not nearly as big as in these photos) and a larger applicator tip wouldn't fit in between the panels to inject the glue. I've also had success with it on other small projects, though I want to be sure to use something that will last on this one. I'm all ears if you have any suggestions. The smaller gaps also make cleaning and sanding between them nearly impossible, but I will make sure to clean any old adhesive/junk out as best I can.
Thanks again,
Ryan