I did this last year, OP.
I loved the idea of backwards hangers then get rid in a year but, like you, I didn't have a year.
I took everything out. I started off by getting rid of everything that I hadn't worn in the last 6 months. No excuses of "I might wear it one day", nope, if it's not been out of the wardrobe in 6 months, it needs to go.
Of everything remaining, I grouped everything that was similar (e.g. all black cardigans together, all blue jeans together, all summer dresses together) and forced myself to pick one of them to keep because I don't need 6 pairs of blue jeans and 10 summer dresses.
It also helps to try things on as you're doing it and brutally asking yourself "does this look good?" For me, half the time the answer was no!
You need to be brutal.
I only gave myself 90 minutes to get it done so that I had to make snap decisions and couldn't dilly-dally over individual items.