Get a laundry bag for washing clothes in. Loose, open weave that lets you toss in a load to wash without letting anything get out. Something like this:
https://www.laundrybag.net/cgi-bin/commerce.cgi?search=action&category=MESH
Just wash your rope inside the laundry bag, set the washer for heavy soiling, with no spin cycle. Use a hefty dose of regular laundry detergent.
You'll get a clean, wet rope, with only a few tangles, and not much time or money spent on it. Wet ropes dry without any special effort, and spinning them will probably shake the washer to pieces, since the load will almost certainly be off balance with a rope inside one laundry bag.
Last white pine we did, I thought the rope was ruined. A few days use, and it wasn't as sticky, but it was still stiff, dirty, and difficult to use. We washed it as described above, and it came out fluffy, soft, and white.