Have you tried contacting John Barton? I believe he was commissioned to make GTF and Kopy Kat cases. Maybe he can make a taller lid with an accessory cap for you.
Another option you may want to consider is having an accessory pouch with velcro made so you can strap it to the case. During play, I use the lid for my It George cue case as accessory cup when I dump stuff out of the accessory pouch. I usually put my keys, cellphones, pens, and any other loose stuff so it's easier to keep track.