I havent tried this with my traditional kilt yet, but it is how I clean my wool sweaters.

I use a product called Dryell.
Basically it is a do-it-yourself dry cleaning kit. You just put the garment in a special zippered bag with a cleaning pad and put it in the dryer as directed. There is a special stain remover as well for the bad spots. Then I guess you can iron the pleats straight and be off. I am one of those "I trust myself the most" when it comes to that sort of thing.

Just a thought.

The recommendations of asking around and researching are very good, I'd add that you might call the BBB (better business beureau) once you find a potential cleaner to see what kind of track record they have.