Try backrolling your paper to get rid of the curl. It does take several days to work. I backroll the entire roll when I first get it, testing every 2 or 3 days until it lays flat on its own, then I immediately cut it into sheets for storage. They come out of the drawer perfectly flat from that point on.
There are many ways to get precise paper to plate alignment. Alignment pins and some kind of a system that holds your block precisely oriented with the pins is probably the most accurate I have seen.
Here is one solution: