Alright, here is the easiest fix I could find:
BafflingSteveo is correct. If you add a .nosync to the end of any folders/files you don't want synced, then it removes them from iCloud.
So, I have a folder on my desktop with a bunch of pictures in it that I do not need backed up (or other documents/files/whatever). I changed the folder name from 'pics' to 'pics.nosync'
Not only does this protect it from future uploads to iCloud, but it also immediately removes it from the cloud while keeping it on the computer. With this removed, I now have a lot more space available in iCloud and am not constantly inundated with messages about low storage.
You don't need to add .nosync to every file (although you can). You only need to add it to the folder which houses the files you want off iCloud but still on your computer. So, for another example, if you have a dozen large files, you can create a folder called iCloudSucks.nosync and move those files to this new folder.
It is actually a pretty easy fix, although it is still dumb that you can't just tell iCloud to stop syncing without losing your data.
Hope this helped.
*side note: I was on the phone for 40 minutes with very nice people at apple who were unable to help me. If I understood it correctly, their fix was to uncheck the box to sync iCloud. They assured me that, although my files would disappear from my computer, the files would be safely stored in the cloud. I think the plan was pretty much the same thing as moving everything to an external storage device, un-syncing and then moving everything back, except they would have had me use iCloud in place of the external storage device.