I am fairly well versed in CM and have been basically using CM in my homeschool (although I am by no means an expert since we have just started homeschooling). I just recently read the 1st version of LCC. I have to say that it would be very easy to use LCC in a CM manner. So, you could read his suggestions and then have the children narrate. LCC suggests reading a few books carefully which is very in line with CM methods. Usually, you are only supposed to read a few pages of each book per day.
As far as the extra subjects, LCC states (I don't have time to find the exact quote right no