Sending reminder for LOR and asking them to do it early?
You sent "all the information" - including deadlines?  You can expect that they will submit by the deadlines that you told them, but not necessarily before. 

If you need the letters earlier than you originally said, you'll just have to ask them - no way around it, and the sooner the better.  If your new deadline is still at least a few weeks away, it shouldn't be too much of an inconvenience for the professors.  If you tell them "You know that letter I asked you to submit in December?  I actually need it tomorrow," they will very likely get annoyed, and may not be able to have it ready in time.