I used to manage when that was what was provided where my horse was stabled. Honestly, I don’t know how. And I now find myself back in an almost worse predicament and was thinking last night that I should make a post here to see if anyone else has a solution LOL!
Due to allergies, I put my horse on pelleted (crumbled/whatever) straw this summer. Worked great. Picked and mucked exactly like pine pellets. Yay! Then came late fall and shorter turnout hours and a few days inside due to garbage weather. All that has conspired to create a disaster zone. She was down to mats every day no matter how much additional money I threw at her stall in the form of bag$$$$ of pelleted straw.
I recently switched to dust-extracted fine (2") chopped straw. Great! It’s cheaper than pellets for more volume! It makes an absolutely lovely bed! I mucked cows on chopped straw for years - this should be a cake walk. Nope. It takes me forever 
One thing I contemplated last night was a 2-implement method and I may try it tonight and report back. So, I’m envisioning basket fork in my left hand and a mini rake in my right hand to rake poo balls out from between perfectly clean straw and into my basket fork.
I have varying success with wall flinging. With the straw being so soft, some of the balls just sink down so I end up doing it twice. Annoying!