The run capacitor is in between the run and start winding. If I read your OP correctly you are decribibg two ways to do the same thing. Most of the time there will be two wires on the common of the capacitor. One comes from L1 the other goes to the run winding. The other wire on the capacitor of corse goes to the start winding. L2 goes straight to the common terminal. You could run two wires from L1 on the contactor and have one go to the capacitor and one go to the run winding. Same thing more wire.