Clarity

I recently brewed (if you can really call it that) a couple of batches of Apfelwein. In the first, I used Red Star Montrachet yeast as was recommended in EdWort's recipe on the cider page. This batch settled and cleared very quickly after fermentation had ended. In the second batch, I used champagne yeast. This batch fermented well, but it has been setting in the carboy for over a month with very little change in clarity. It doesn't seem to be settling hardly at all.
Is there a way to speed up this process? Cool it down? If so to what temp. and for how long? Any other suggestions short of filtration or waiting for a year?

If fermentation is finished, you could try cold stabilization. Usually, my basement temperatures cause the particulate to fall right out and clear up.

Different yeast will react differently, and compact differently affecting clearing times, as you've seen. My personal suggest is to wait. Firstly, it shouldn't be too much longer to clear up. Secondly, giving it another week or two, or a bit more, will only help you out, as it's forced aging time.

But if you must have it clear now there are options. You can cold crash it, by keeping it at a very low temperature, in a fridge or outdoors. Or you can use clarifiers such as sparkaloid. Get the hot mix sparkaloid if you are going to use it, use as per the instructions and you should get some crystal clear brew in short time.