Hi Nicholas,
First question - whether project team got some control over EEF? To me, not directly, but like you mentioned, if the organization adopted the lessons learned and implemented as company system, which becomes a constraint to project, then yes.
Second question - exception on EEF as input to certain processes? To me, the way I look at it, if EEF will affect the process, then I'd say I need EEF. For example, when you are monitoring your work, would you need EEF? You need PMIS for M&C and for PICC, that's why you need EEF as input. Other than that, you won't need EEF for all other Control Processes. It all ties back to what each particular process is all about, and what you want to achieve by doing that process.
Sorry for late reply, as I was busy studying for the exam.