The CM-7777 is a 'fringe' to 'deep fringe' preamplifier. Your signal conditions are not 'fringe'.
Sadly, the Channel Master specifications do not provide a maximum input value that would allow your or I to calculate how close to overload your signals plus antenna gain would cause the CM-7777 to operate at.
BUT, I doubt you will solve the reception reliability problem with any amplifier. If you have an oak tree in the way, and you are already using high-gain directional antenna. You don't have a problem with low signal levels, you almost certainly have a problem with 'foliage induced multipath interference'. The solution is, find a mounting option that gets the antenna above or around the tree(s)... or get a chainsaw.
Back to the idea of a preamp... perhaps, if you have many TVs connected, a distribution amplifier might be indicated... But the conditions shown in your report jump off the page saying 'No preamplifier needed'. The CM-7777 has been redesigned... it's entirely possible the 'new and improved' version is less tolerant of strong signals.
Even the Channel Master ad copy cautions against using the CM-7777 in conditions like yours:
http://www.channelmasterstore.com/v/...4jan12_web.pdf