Have you checked the DRL relay in the fuse box under the dash? Low beams run through this since DRL's use low beam side to run.
Low beam runs from the switch to the cluster, from the cluster to the DRL relay.
Tap on the DRL relay and see if it affects the lowbeams or jump the LT GRN/BLK wire to one of the ORG wires at the relay.
Not that I know of. Low beams are the dark blue wire comming off the switch. I have seen this wire melt at the connector before. Hook the voltmeter up to the dark blue wire at the headlamp and wiggle the dark blue at the switch and watch for voltage dropout.