How long will the shaft be? We have also planned a shaft from the future bathroom to the heating room (ground floor, directly opposite are the washing machine/dryer, ironing board, clotheslines for drying). I don't think it really needs to be cleaned intensively – and even if it does, you can surely repurpose a long brush (chimney sweep :cool).
The really dirty laundry "happens" on the ground floor anyway: muddy clothes from outside, various towels (often used during construction work…), dirty tablecloths/upholstery after garden parties, etc. In addition, when something is soaked, it is done directly between the washing machine and the sink in a small tub. None of that has to go through the pipe. Carrying it upstairs is also done the easy way: The new dressing room is right next to the elevator shaft, which is conveniently only 2m from the "washing mile" on the ground floor. No more lugging.