Wow, I never thought about fitting the rephone somewhere like that. Now I’m super curious if I could fit it in my Nokia 7110!
And about your project:
A thin plexi or other plastic is way much better to fit the screen, fiberglass pcb materials are hard to work with, they break, etc. I would redo that part, that could save space.
The sound: I would move the mic down to the headphone jack connector, and do you suffer from low speaker volume? The gbc has a lot of space, and a little mono amplifier could be placed anywhere.
And the tricky part: the battery. You should buy 2 AA lithium rechargable batteries (there are many counterfeit, bad ones, beware!) and the trick: don’t even try to connect them in series! Try to move the springs to one side (probably it will end up in soldering) connect them parallell, and voala, you got a really kickass huge battery pack. Don’t worry, even laptop batterries are connected parallell in pairs, it will work.
Last but not least: cool USB connector