Andy here's a thought,
a friend has just bought a 5d mk iv and asked myself to set a few things up on it, bbf, frame rate etc
testing I found it to have a slow fps approx 4 instead of the claimed 7 fps.
I adjusted loads of the jpeg settings to off, why when she shoots raw?
Remember that the display screen will show a jpeg and so even shooting in raw these jpeg settings still take place.
These setting do take a toll on the processor as they are happening whilst also recording the raw file.
I turned off things like highlight priority and also anything that you can post edit with a raw file.
The frame rate certainly is better now.
Give it a go you never know.
Another thing to check is that in menu 5 (2nd from left) C.Fn4
rive
The continuous shooting speed is set to its max.
I can't remember what the default is set to but maybe its set not to shoot the max which when set shows as; High speed 14(16) shot/s
The brackets are for when using mirror lock up.
Below that are other options to set the shooting speed, Low, Silent HS/LS
I found when trying to use the CF function I couldn't use CF 2 & 3, George gave me the answer that it wasn't set to be available in the menu and maybe this is the same on your mkii that the speed in the menu is set to a low speed?