Looking to do my first 2-week bikepacking trip in the North West

Hey, first post here. Two friends and I are looking to take a two week trip out on our 29ers. We currently live in Brooklyn and are jonesing (craving) to escape civilization for a bit before returning to school/work. I have kinda taken on the responsibility of setting up the trip but, I'm not really sure how to go about it though.
We all have significant hiking/camping experience, but never on bikes.

We would like to go during early September for 9-10 days. We are taking hammocks, and would like to do primitive camping (aka not a motel). The same goes for our trail choices- ideally we would ride 3-4 days straight in a wilderness-esque setting (aka not highways). Then being that we are observant Jews, spend Saturday (Shabbat) in a motel, because we cant ride on Saturdays. Then, Sunday head out for another 4-5 day wilderness bikepacking adventure.

We would like to do something in the Olympic mountains, mainly because of the rainforests. I saw they have a trail called the Olympic Discovery Trail, but it seemed like too much time spent in civilization. If anybody has any ideas, itineraries, or tips, it would be greatly appreciated. It doesn't have to be in Olympic park, anything in the NorthWest along the Pacific works too (as long as it involves being out in the beautiful forests of Mother Nature).

Thanks in advance and G-d Bless!!