Tom W,
Up early today ?
You can call any detail shop you want, but I imagine that they wouldnt do anything that you can't do (not sure if you have a garage available...)
http://www.peachparts.com/shopforum/detailing-interior/114518-how-dry-wet-car-carpet.html
there are a few ideas in that thread. When my "monotheistic nonprofit" was recently flooded, we hired a company to dry all the wetted carpets - all they did was open the doors and bring in some large fans that blew along the floor (one large fan per room - they were those squirel-cage high velocity fans...they were there for most of 2 days) I think that they periodically moved the fans around so that they caught every part of the carpet, but a Miata interior is pretty small - any fan would probably do.
I have done the "shop vac to suck up water" idea, and it will pick up a lot of moisture if you spend some time with it.
-John