I have to agree with swirlchaser, it appears to me that your putting the cart before the horse and may be compounding the problems. Going to the heavier line may not even solve your issues.
As I said before, I've cast 2/0 size Clousers with a 6 wt, just not very far, and I've been fly fishing for a long time. It can be done, but it's not the best size to be casting with that rod, especially if it's heavily weighted.
For the waters I fish, which are shallow, I often tie 2/0 size Clousers with light wire hooks, and/or small size barbell eyes, or even bead chain which certainly makes a difference in the flies final weight. I have cast this size on my 6 wt, tied on regular saltwater hooks & heavy eyes, but from a boat, and again, not very far. Usually no more than 25 or 35 feet, because the fish would be near the boat, so longer casts were not needed. I remember a situation several years ago, where I had been fishing for perch, in an area that is 10 to 15 ft deep and found Striped Bass & Bluefish chasing schools of baitfish near my boat. I re-rigged with 3 ft of straight 20 lb line and a large Clouser, probably 2/0 because I use this size often, but I don't recall the exact size, and caught several decent size fish within 25 ft of the boat. I had been using a sinktip line, so all I needed to change was the leader. This does not happen often, and I would have preferred to have had a heavier weight rod, like a 8 or 9 wt.
I still have not seen that you answered my question about your leader length. How long is the leader you're using?
Ive also noticed that my line doesnt seem to pull out very smoothly
What exactly do you mean by this? How much line are you stripping from your reel before you attempt a cast?
You should be stripping enough line for the length of the cast that you intend to make plus slightly more, which will end up as slack between your line hand & the reel once the cast has been completed. If you're attempting to cast directly from the reel at all, well, it won't work!
An experienced caster can strip line while false casting, but it's usually not necessary, unless attempting a very long cast. As I said before, long casts are not necessary for your situation, and not advisable with a 2/0 Clouser & your rod.
Also, does the reel have an adjustable drag, and if so, how tight is it? It should not be set so tight that it makes turning the spool, or stripping line difficult.
How full is your reel? If the line is touching the inside of the reel frame, and binding to keep the spool from turning freely, that would be a problem too.
You should also make sure that when you wind up the line onto the reel, it's as evenly distributed on the spool as possible. Otherwise, you'll end up with high spots which could bind against the inside of the frame, or they may even create a backlash type situation, which would cause problems for you.