Hey Xan, I don't think that you can use the Work = Force x Distance calc in any case, as the force is a function of band elongation. The energy would be the area under the graph of force vs elongation,
so you would use Grossetti's function of 1/2kx^2
But Grossetti's calculation is flawed because stiffness is inversely proportional to length.
As k=EA/L, and the theoretical roller gun in Dan's example has a rubber length of twice the normal gun, its stiffness is half of the single band. As there are two parallel rubbers for the double band gun, its stiffness is twice a single band.
Stiffness
Single band k = 1
Double band k = 2
Roller band k = 0.5
Elongation
Single band x = 1
Double band x = 1
Roller band x = 2 (as it is half as stiff, you can stretch it twice as far for the same loading force)
Energy
So applying E=1/2kx^2
Single band E = 0.5
Double band E = 1
Roller band E = 1
So Dan was right all along.