Get a wet and dry vac, good fabric shampoo and do work. Best just to wet the fuck out of the seats, if there's a clear nozzle on the vac then you know when your done by the water colour you're sucking up.
If you're brave and have a dehumidifier then power wash them. I'm not sure how good it will work for alcantara but I've done a few car seats with a power wash and stuck a dehumidifier in the car for a few days and it shifted lots of shite.
1)What i do is make some upholstery cleaner in a trigger bottle.
2)Lightly spray the seats
3)lightly scrub the seats . the upholstery cleaner should foam up(the foam is what brings the dirt from the seats)
4)Wet Vac the seat to remove what you can from then seat
Directions as above but ensure its upholstery cleaner and not a general APC...needs to be low foaming otherwise you will be repeatin the extraction process many times.