oh my.. does your problem bring back memories.. I also have my sewing room in the basement.. I had nearly the same thing happen to me.. I was so upset..
I took the piles of dripping fabric upstairs in laundry baskets.. some of the long pieces I left folded and used safety pins to pin the folds together.. small pieces I put into mess bags.. and I began to wash them with white vinegar in the water..
The thing to realize is that what's on the fabric is water.. so you don't have to agitate them like you would if you were were washing play clothes.. All you need is warm water, a bit of laundry soap, the vinegar, the shortest wash cycle your machine has.. and then spin them out really well.. some I even turned the knob around and sent the load through a second high speed spin.. the spin doesn't tangle or ravel your fabric, it's the agatation that causes you problems..
I un-pinned the fabrics I put into the dryer.. some of it I spread out on the floor, on the back deck.. every place I could find.. I had so much I didn't dry everything iin the dryer bone dry.. but took it out half dry and spread it out someplace to finish air drying.
I was surprised that all I really lost was a lot of time and some soap and water.. Wish all that lugging up the stairs and washing, drying, & folding would have taken a few pounds off, but I didn't even lose that!!
I know it's a horrible mess, but just don't let it sit and it will all be okay.. Fabric is too expensive not to take quick action on.. I hope your mess comes out as well as mine.. If I were closer, I'd come give you a hand.. I know it's a lot of discouraging work..
On the plus side, you get to review your stash up close and personal.. and you can even actually get your stash in good order before it's all said and done. Good luck!