That was my first thought. And that's a relatively quick 'n easy version, I think you could make a much more compact version using a smaller Arduino and a breakout version of the FONA instead of the shield. Replacing the TFT touch-capable screen with a little OLED and physical buttons for dialing would also help and increase battery life (their 2 keypad options don't look well suited for this tho').
Using the shield form factor in the guide made it relatively easy to hold all the pieces together. Using smaller components would cry out for a case to hold them together.
Yep, great idea to use a little OLED and go for something smaller. You might check out the Metro 'mini' board or other similar small Arduino boards like the Micro, Mini, Nano, etc. too: https://www.adafruit.com/product/2590
Using the shield form factor in the guide made it relatively easy to hold all the pieces together. Using smaller components would cry out for a case to hold them together.