I did the same thing as you!
(except my engine didn't stall)
I got stuck on the crossmember and had to get pulled out and I had water up to the top of the passenger seats
I pulled up my carpet and took it to the car wash and used their high pressure hoses with soap and just pressure washed them.... they are still sitting out to dry
They have been sitting out to dry for 4 days... the carpet was dry but there is foam in the back covered with plastic sheeting.... it won't let the water out of there
I pulled off the foam on the back cause it was still soaking wet... I'm just gonna re-glue it back when it dries.
by the way, it wasn't bad to pull the carpet. It worked out well for me anyways because it gave me incentive to actually get my sound deadening material installed