When flying a circling approach, is it permitted to begin the visual circling segment prior to the final approach fix?
While researching this subject, I found a few things that shed light on the subject:

Procedures

FAA ATC Order 4-8-1 Note 1 says:


  1. Clearances authorizing instrument approaches are issued on the basis that, if visual contact with the ground is made before the
  approach is completed, the entire approach procedure will be followed
  unless the pilot receives approval for a contact approach, is cleared
  for a visual approach, or cancels their IFR flight plan.


So we have to follow the entire approach, which includes all mandatory altitudes.

Aspen Approach

AIM 5-4-20. Approach and Landing Minimums says:


  c. Straight-in Minimums are shown on the IAP when the final approach
  course is within 30 degrees of the runway alignment (15 degrees for
  GPS IAPs) and a normal descent can be made from the IFR altitude shown
  on the IAP to the runway surface. When either the normal rate of
  descent or the runway alignment factor of 30 degrees (15 degrees for
  GPS IAPs) is exceeded, a straight-in minimum is not published and a
  circling minimum applies. The fact that a straight-in minimum is not
  published does not preclude pilots from landing straight-in if they
  have the active runway in sight and have sufficient time to make a
  normal approach for landing. Under such conditions and when ATC has
  cleared them for landing on that runway, pilots are not expected to
  circle even though only circling minimums are published. If they
  desire to circle, they should advise ATC.


The key part for this discussion is that, for approaches that would be straight-in if it weren't for the high descent rate on final (like the KASE approach), pilots are not expected to circle even though only circling minimums are published. If they desire to circle, they should advise ATC.

Well, in this case we can't land straight-in after making the last crossing restriction, so what can we do?

Combining the two quoted passages, our options are:


Get approval for a contact approach
Get approval for a visual approach
Cancel our IFR flight plan
Get approval to circle since we can't land straight-in.


The first three are pretty straight-forward and can be used if you pick up the airport visually in time.  

If you need to circle, I found a great article called Circle-To-Land Tactics which was written by a former chairman of the ALPA TERPs committee.  He suggests overflying the runway and then flying a modified pattern:



Teterboro Approach

We can't start our circle until we are within the protected circling area.  This means that for my category C airplane, I have to wait until 1.7 NM from the runway threshold before I can begin my turn.  

We could make a right 90 degree turn followed by a left 90 degree turn to line up on final, but that would eat up about one mile just by turning.  Since runway 1 is actually closer to us than 6 at this point, I have even less distance to work with and can't even see the runway during the first turn because we are banking the wrong direction.  This would be pretty tight.

In this case, the previous article recommends a circle like this (which would be modified for our actual runway layout):



In good visual conditions, I would just ask for a visual approach so that we can start the turn a little sooner and land "more" straight-in without flying all over the airport.



One last point:  Since there is a control tower at both of these airport, make sure that they know what we are going to do!