WOW, this sound pretty bad.
Since I can't see how bad the seat fabric is, I can tell you that I have had better success with a mild solution of dish soap and water such as, Dawn/Palmolive etc. I have also used a very, very mild solution of electric dishwasher detergent as it has some bleach in it. And I've used it without damaging or bleaching out the fabric.
As you know/may not know, that the more soap you use, the more soap you'll have to remove. And any soap left behind will only attract more dirt.
You can Youtube...
Sweet Project Cars
&
Dallas Paint Correction and Auto Detailing
Both have some great videos on all detailing projects. I think you'll find something in either one.