Sorry to necropost, but as I'm late to the Moolti-Pass game and just getting started on this kit, I've been researching ways to make it light up.
A couple of thoughts come to mind. First, when using a lithium coin cell, it's actually not necessary to use a series resistor for the LED--the battery itself has enough internal resistance to limit current. This is not the case for flashlight batteries, the use of which would require a resistor.
Also, I think I'm going to try to use a thinner lithium coin cell, such as a CR 2016 or CR2025. The battery's number tells you about it's physical dimensions, with the first two numbers giving the diameter in mm and the last two the thickness in tenths of mm. So, a CR 2032 battery is 20 mm (2 cm) in diameter and 3.2 mm thick. A CR2016 is 20 mm in diameter and 1.6 mm thick.