Is a hold in lieu of a procedure turn specifically one hold on an RNAV approach?
When flying a hold-in-leiu-of-procedure-turn and the exemptions from that procedure are not met, you must fly that procedure exactly once. From the AIM, 5-4-9(a)(5):


  The  holding  pattern  distance  or  time
  specified in the profile view must be observed. For a
  hold−in−lieu−of−PT,  the  holding  pattern  direction
  must  be  flown  as  depicted  and  the  specified  leg
  length/timing  must  not  be  exceeded.  Maximum
  holding  airspeed  limitations  as  set  forth  for  all
  holding 
  patterns apply. 
  The holding pattern maneuver is completed when the aircraft is established on the inbound course after executing the appropriate entry. 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.


Further notes: I'm not sure quite what you mean by losing 2000 feet in "half a hold", but if you got a clearance to maintain 4000 until established, you could start your descent immediately after crossing ODAZO, giving you 8 miles plus a one-minute turn to descend. At 120 kt, that's 4 minutes for the 8 miles, so 5 minutes for 2,000 feet or 400 ft/min - perfectly reasonable.

Finally, you mention that "When directed by ATC to fly a straight in approach, the hold-in-lieu is not required." Your statement should be stronger: as when NoPT is printed on the chart, a straight-in clearance forbids the procedure turn/HILOPT unless you ask for and receive approval from ATC.