Exactly the same story for me on the squat. I sat back and used my PC for so long to avoid being "quad dominant," not realizing that my quads were super weak and I was totally PC dominant haha. It's weird to force your knees/hips forward when you're used to sitting back, but it feels awesome when you get the hang of it. Just watch a million oly lifters squat, seeing them do it helps you when you try to imitate it, i swear. Seeing over and over helps you learn.
As for the clean deads, I'm glad you're gonna mess with them, I think they're better long-term to work on your weaknesses. It's not exactly "squatting the weight up," I wouldn't think of it that way cause that's gonna screw you up. I'm no oly coach, so again I would suggest checking out some olympic lifters doing deadlifts... Clarance, the vid I put in, is a really strong kid with great form so check him out, learn what you can, emulate. Basically, the clean dead uses the same muscles as your normal dead. Difference is gonna be that you'll want to really push your knees forward at the start, very different from the "vertical shins" cue you hear in powerlifting, and keep your back flat. Especially with your style dead, you might have to use some pretty light weight in order to keep the back flat. Breaking the weight from the floor, the emphasis should really be on your quads until about mid shin, then you start to shift your knees back , really use your lats to keep the bar tight to your body, and let your back/PC take over to finish the lift. The greater emphasis on quads at the start will be good for you, and then forcing your to keep your back flat so that you can better use your butt/hamstring AND increase the weight at which your back NEEDS to round should be good too.
If you check out that video, you can see he's definitely not "squatting the weight up." He pushes his knees back and uses a lot of back/PC as well as quads.
Here's another good video, you can see how far out he pushes his knees at the start, as well as how he shifts his knees back and sweeps the bar into the hip. This is a clean pull, however, so it's a little different at the top.
You might even want to mess with doing a hook grip, if you're starting with lighter weight for a while. Personally, I like hook gripping a lot - it lets your shoulders hang in a different, slightly better position with heavy weights that I like - and I'm gonna start switching all my deads over to hook grip this summer I believe. maybe you'll hate it haha, but it could be worth a shot. Good luck with the learning and experimentation my friend