There are no auxillary parking lights, highbeams do not share a common ground. This wouldn't fix the problem since its the computer that kills the power to the lowbeams. It actually kills the +, not the ground.
2) Yes, resistors will work, so will higher gauge wiring. But if we were to go as far as to do that, its probably easier to take the aftermarket DRL module out and bypass the problem entirely.
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Hot: 2001 Estoril M Roadster
ZCP 19's michelin supersports, ZHP knob, JL 8W3
Cold: 2002 TiAg M3 6mt ZCP 19's michelin supersports, deoranged, dechromed, led tails, ZHP knob, UUC SS v3, GROM, OEM 18's w310's,
Fun: 2006 YZF-R6, black