Run new cable from the amp to the input of the crossover. Run new cable from the tweeter output on the crossover to the tweeter - can run this cable easily with the dash top off.
Then run new cable from the crossover woofer output to the back of the head unit. For my Alpine head unit, I cut the wires from the Alpine > Renault wiring loom that carry the feed to the left and right woofers (4 wires L and R + and -). From what I remember these were white + white/black and grey + grey/black for both sides, might be different for Sony/Kenwood etc. Join the Renault end of these cables (which lead to the door woofers) to your cables that have run from the crossovers. Bit of extra wiring but it makes it all easy to get to. Make sure you cut the Alpine > Renault loom though so your original car wiring is intact.
My crossovers were small so I could tuck them in the corner of the footwell and tie them to existing cables. Loads of room under the dash otherwise, take it off and it will make things much easier.