You can use the regular parcel post option as well with USPS.
I don't know about the media rate though. Looking at the files and the USPS Shipping Assistant...maybe you could try and add a "Media Mail" option and test it out. Look through the files in /store/library and find the ones that you are using for your cart. Copy and paste the sections for Priority Mail and then just change the name to Media Mail. You will need to do the same with the order form you are using. The worst that can happen is that it doesn't work, but it just might.
Be sure to make a master copy of the GOOD and WORKING files before you start. I like to put them in a folder named "Store Master" and make all of the files read only. I've goofed up a number of good files in my time and that will keep you from ripping your hair out.
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Carol aka SouperMom
http://www.soupermom.com