Am I required to report entering the hold in lieu, persuant to the IFR mandatory reporting points?
If you're in radar contact with ATC, the answer is no, you will not need to report it unless requested to.  If you are not in radar contact (which would be unusual as that is in Class E airspace) you would not have to report your position entering the hold at YAYUB unless you were instructed to hold at this point with an EFC time.  From the AIM 5-4-9


  When a holding pattern replaces a procedure turn, the holding pattern must be followed, except when radar vectoring is provided or when NoPT is shown on the approach course. The recommended entry procedures will ensure the aircraft remains within the holding pattern’s protected airspace. As in the procedure turn, the descent from the minimum holding pattern altitude to the final approach fix altitude (when lower) may not commence until the aircraft is established on the inbound course. Where a holding pattern is established in-lieu-of a procedure turn, the maximum holding pattern airspeeds apply.


But 5-4-9 also states that 


  If cleared for the approach prior to returning to the holding fix, and the aircraft is at the prescribed altitude, additional circuits of the holding pattern are not necessary nor expected by ATC. If pilots elect to make additional circuits to lose excessive altitude or to become better established on course, it is their responsibility to so advise ATC upon receipt of their approach clearance.


You would have to report leaving YAYUB inbound and to report crossing WIKUV FAF inbound as well.