The BPs have *never* been part of the MC and the guy that came up with it on the MC didn't really have a full understamding on how they work. Read the link below for a more thorough explanation. If you read the FAQs you will have also read that dehydration is also not the only factor of why the BPs are not a good idea on the MC.
Doing the LF in the Middle of the MC is just not done. First it has the potential to make you violently ill by dumping all that oil in the system in the middle of the fast and second the Epsom salts are very dehydrating and that is something you don't want to happen during a fast. Fasting works by giving the digestive system a rest and throwing in all that oil in the middle of a fast will bring the fast to a screeching halt and like I said before possibly make you very sick.
The wisdom on the LF is to wait a week or 2 after the MC and introduce fats to the diet gradually to let the system build up some bile to have a more productive flush.