Coffee filter may be a bit much, imo. What pulp there is would back it up quickly I imagine, especially in the quantities OP is describing.
The jewels/pips of a pomegranate, though small, contain quite a bit of juice and isn't the pulpiest of fruits, but the seeds are the real dilemma. I would roll em whole to loosen things up, half them and beat em(on the outside) with a spoon to get out the goods. From there, maybe just a blender, and then run through a chinoise. A technique for smaller batches that works well is to put the pips into a zip top bag and roll with a rolling pin, then strain.
For really big batches, get all the little ruby bits of goodness and put them in a pot. Cover with just enough water to cover and bring to a simmer. The pop all on their own and just leaves you to strain. If you are going for a molasses, this may work best as you are going to have to cook it down substantially anyways.