As for a firing mech, a simple ratchet could be implemented in the top bar/rail, released by a lever system originating at a trigger on the handle at the front. This means a compact bullpup design with all the technical gubbins behind the trigger, embedded in the stock. This leaves more room for stretching the bands, which will likely be attached to a bow in front of the handle.
Anyhow, please leave any feedback in the comments, and I will be sure to update this 'Ible with any progress I make.
(Obligatory notice - my first post: be gentle.)