Well I do have an idea, which I posted in the top video games never made thread.
But honestly if you can add the Wonderswan's CPU in place of the Zilog along with its RAM, while all models would need at least 2 AA batteries to run, I think we could put the 10-20 hour lifetime, but one feature I feel the need to retain is either backwards compatibility with the game gear or the ability to turn off the backlit screen.
SEGA Exodus
Release Date: November 10th, 1997.
Dimensions: 3.25 backlit screen, Sega Genesis D-Pad, 6-face buttons (A,B,C,X,Y,Z), 2-shoulder buttons (L and R on top). The Shell itself is designed to resemble a large Sega Saturn Controller. While still large enough to be visible in your pocket, the size is still about 1/8th the size of the game gear.
Game Storage: ROM Carts similar in size and design to the Game Gear Carts. Capable of holding up to 8MB of data in the carts. Backwards compatibility for all Game Gear games.
Main CPU: Zilog Z8116 16-bit processor (manufactured by NEC.)
Price: $250 at launch. $30 for every game sold.
But honestly if you can add the Wonderswan's CPU in place of the Zilog along with its RAM, while all models would need at least 2 AA batteries to run, I think we could put the 10-20 hour lifetime, but one feature I feel the need to retain is either backwards compatibility with the game gear or the ability to turn off the backlit screen.