Expediate,
Don't mix requirments for CPL issue and the pre-entry requirements for the FI course.
For CPL issue (modular) you need 200 hours total with 100 p1, as you say by the time you have done the CPL skills test you may only have 179 hours if you completed everything in minimum time. The remaining hours do not have to be p1 it can be dual which you have correctly stated, most people will use the time from the IR course to make up the hours.
However the pre-entry requirement for an FI rating is hold a CPL or have 200 hours and 150 p1 if a ppl. If your CPL is not issued then you do not hold a CPL, you have a PPL hence need 200 hours with 150 p1.
Knowing the pedantic nature of the authorities the wording would read passed the CPL skills test, if you did not need an issued CPL.
For all those from the modular route the 200 hour requirement is irrelevant as if the CPL is issued you must have 200 hours anyway. Therefore this ensures all FI candidates have 200 hours.
The only thing that has caused confusion on this thread is we have some integrated students whom didn't get a recommendation from their flight school to a major airline and now have to consider instructing, consequently we have CPL holders with less than 200 hours total time, who reading betweem the lines in Lasors are eligible to start an FI rating as they hold a CPL.