Definitely get the one piece set up - it sits under the saddle much better than two separate pieces, far less bulk and no shifting around.
I have multiple of the Lemieux Merino with sheepskin backing - one is about six years old. It has been used daily on multiple horses and it still looks less than a year old.
I do not machine wash mine. I put them in a bucket of cold water before I ride, with a glug or two of whatever soap/shampoo I have on hand. Mix around and soak, while I ride. When I’m done with my ride I hand-stir and then take a Tiger tongue (a sponge will do but not be as good) and scrub the dirty areas vigorously. Rinse/hose off and hang out to dry. This doesn’t make it “show quality” clean, but it does make it perfectly clean for a clinic or lesson. I have a black LeMieux that is reserved for shows.
If you brush out the fur + dirt after every ride, you’ll be surprised by how infrequently you need to wash the pad. I might wash mine once a month in the summer if it gets really sweaty, but usually only wash a handful of times in the winter.
I agree with your fitter that sheepskin directly on the horse is much more comfortable - my horse seems to really like his sheepskin pad over Thinline, even though I think the Thinline does a better job of concussion absorption. He will nose it while it is hung over the fence and seems to really enjoy being “pet” by it.
I would be alarmed that you have hard bumps on his back. Can you get a second opinion that the saddle fits…? Are you sure they are not bug bites?