If one does not want to clean the whole coop out yet, the first thing to do IMO is to remove just the most egregiously damp or pooey parts, and then add a buncha fresh shavings, and keep adding fresh clean shavings as needed (likely every few days or week). That often helps a lot.
That said, as I keep saying on these deep litter "method" threads, there is no ONE deep litter method there are a whole variety of different approaches each with their own pros and cons, and they are not all workable in all situations. So what works for one person is liekly not going to work at all for some other person. You just have to experiment around til you find what's best in your particular coop. And IMO there are really not very many people whose situations (climate, coop, flock, etc) make it possible to do damp composting-style deep litter management over the whole winter (largely because it requires so much more ventilation than most have, or a very dry climate)
Good luck, have fun,
Pat