I called Airsuppliers back to see if they would swap the 68H22624 parts with the original parts I had tried to order, LW-12136. They were after all the ones who told me I needed the newer part, which their system shows supercedes the original. If they were going to tell me to buy the new cushions, then they should also have sold me a new type of retainer, instead of two products that were incompatible.
The woman on the phone was friendly, but she insisted that I would have to ship back the old items and pay $17 and change shipped for the correct ones.
Not exactly big $$$, but this isn't the type of customer service I've come to expect from the places I buy my parts. I ordered the correct parts from AeroInstock instead.
I will NOT be placing any more orders with airsuppliers, and I will NOT be recommending them to anyone as a good source of aircraft parts.