Thanks for all the tips. I was going to go with the strips along the sides, as suggested, to mount the slides to, but then I realized that while I'm fairly certainly everything is square, I realized that if it wasn't, on either side, I'd have a problem.
I have watched a few videos of folks using the rear brackets and and how they install them and it looks pretty straight forward. I felt like using the brackets, I'd have a lot more control on making the slides square.
I have about 14.75" to work with, so I ended up getting some full open 12" slides with the extensions to go with them.
KV 8450FM 12" Side Mount Full Extension Drawer Slide Anochrome Polybag Knape and Vogt as well as the rear mount brackets that will give me enough extension to make it work. KV 8403, Rear Mount Bracket for Various Ball Bearing Slides, Knape and Vogt
Maybe I'll have a hard go of it, but I think I will figure it out. Thanks again for the assistance!