I keep reading about the reconstructed tape but I don't actually see the algorithm CME uses to split large orders up. Does anyone know why or the algorithm used by CME to decide to split orders instead of just reporting the large order as one?

IMHO

If you buy 50, then the order will be executed per the orders that are in the book.
If there first in the queue is 50 or more, then you get one execution.
If there are 10 x 5, you get 10 exeuctions of 5

To optimize the feed, it will be 50 executed (which is not 10x 5

tape recontruction is the opposite, it is breaking down 50 in 10 exeuctions based on the book info