Aspen ODP question

I have a question about the ceiling and visibility minima as
alternates for climb gradients in departure procedures. A good
example is at Aspen (KASE), straight out of the FAA Instrument
Procedures Handbook, but they don't explain the portion I find
difficult to understand. I've duplicated the entire text of the
procedure at the bottom of this message.

So the issue I have is that the required ceiling to avoid the 460 ft/
nm gradient is 3100 feet. That makes an MSL altitude of just under
11,000 feet as the minimum for the bases of the clouds. But, if the
clouds are lower, the 460 ft/nm gradient is to be maintained all the
way to 14,000 feet MSL.

So are all the obstacles below the 11,000 foot ceiling, or not? If
not, how can the 3100-3 minimums with standard climb gradient result
in a safe operation? Conversely, if all the obstacles penetrating the
40:1 surface are indeed below 11,000 feet, then why require the 460 ft/
nm gradient all the way to 14000 feet? I understand that there will
be some obstacle clearance provided by the gradient, whereas the
ceiling can be right on the obstacle, but 3000 feet of difference
between the two seems too much for that explanation.

The old TERPS (in paragraph 1208) stated that "The ceiling value shall
be the 100-foot increment above the controlling obstacle or above the
altitude required over a specified point from which a 40:1 gradient
will clear the obstacle." What does the second part, after the "or,"
mean? And does that have anything to do with the Aspen procedure? I
believe that the newest revision of the TERPS has deleted that second
part and added the description of a visual-climb-over-the-airport
procedure. Is that supposed to be a replacement with different
terminology, or are those two things not related?

ASPEN-PITKIN COUNTY/SARDY FIELD
TAKE-OFF MINIMUMS: Rwy 15, NA. Rwy 33, 3100-3
or 1000-2 with a min. climb of 460' per NM to 14000.
DEPARTURE PROCEDU Climb heading 340° to
8700, then climbing left turn to 16000 heading 270° to
intercept and proceed via I-PKN northwest course
outbound on backcourse and DBL R-244 outbound to
GLENO Int/DBL 22.7 DME. Climb in GLENO holding
pattern (SW, left turns, 064° inbound) to cross GLENO
at 16000 before proceeding in route.
NOTE: Rwy 33, 8179' tree 3447' from departure end of
runway, 1379' left of centerline.

The IPH also has an example of the visual-climb-over-the-airport
procedure, which is very explicitly stated as part of the ODP:
BECKWOURTH, CA
NERVINO
TAKE-OFF MINIMUMS: Rwys 7, 25, 3500-3 for climb in
visual conditions.
DEPARTURE PROCEDU Rwys 7, 25, for climb in
visual conditions: cross Nervino Airport at or above
8300 before proceeding on course.

thanks,

Peter