Component Speakers in door/dash

I recently bought some component speakers to replace the door 6x9s and
dash 5-1/4 speakers in my 2002 Caravan. I'm having troubles figuring
out how to run new speaker wire to the door speakers. I see there's a
wire harness where the door meets the door frame (for removing the
door, I guess?). I could probably either use or replace the speaker
wire from the speaker to the harness, but I'm not sure how to get the
wire from the crossover to the harness on the door frame side.

Has anyone done this or did you come up with another solution? I'm
also looking for tips on where and how to mount the crossover. Looking
under the dash, I'll probably just strap it to something on each side,
but again, if you came up with a good spot / solution, I'd appreciate
any tips.

Thanks!