Have you tried canned pumpkin (NOT the real stuff, for some reason, it HAS to be the canned version)? And what about Rescue remedy in her water - or place a few drops on here fur where Tigger will have t lick it off. It does not have the ill effects some tranquilizers have. I am a physician so am loathe to give my cats sedatives unless they have no adverse effects. Cats on even small amts of sedatives can fall asleep and suffocate under something, have their breathing affected or fall because they are unsure what they are doing. Of course if you cab watch them fore the entire 12 hours plus a sedative's half life will be in their system or pick one that has a short half life. And whatever you do, DO NOT give her gravol or Valarian and really nothing without talking to your vet first!
Cocculine is also good- no adverse effects at all.
However, with cocculine or rescue remedy, she may fall asleep or at least be calm enough for you to do a little at a time. I would start with a bit and work up to more each time. You could also hire a professional (vet - not a groomer who knows nothing about meds) to do it for you. Or have the vet sedate her properly and then bring her to a groomer to get rid of the mats. with ferals, it can take time and patience. I shd say is almost a;lways does actually.
"There are two means of refuge from the miseries of life: music and cats" Albert Schweitzer