Wiring for long runs
As ThreePhaseEel has suggested and since its already installed maybe you should think about what your really need (demand verses connected). One thing you could do is install an extra conductor to your run to the jbox and get one circuit to the pagoda and one circuit to the shed. Also I would rethink my conductor size to the j-box. Having a #6 run 110 ft to a #12 running a further 90 ft wouldn't be my idea of a good circuit. To be sure you would have to do a drop calculation to the j-box and then another to the shed. In other words I don't see the benefit of running the #6. Also FYI a #6 does not fit in a standard 20 or 15 amp breaker. The largest they  accept is a #8. So you would have to splice another tail on to it in the panel.

I have also done what everyone has suggested. Only I have installed a buck/boost transformer. You could install it either at the load or line side of the circuit, and simple boost the voltage to whichever % your going to need to cover the drop. Remember you would have to do a voltage drop calculation with the necessary amperage at each location to get the proper boost. Also remember that  even though you adjust the voltage you will experience a power loss due to the resistance of the wire.

Example: If you installed a boost xfmr to cover a 10% loss. Then you would loose 10% of your power.  120V*20A=2400VA(W), less 10% would be (120V*20A)*90%=2160VA(W) or 2160W/120V=18A. See how it works.

Good luck on whatever you decide.