Average Agility of Kiril, Fury of Beasts?

The average agility gain of the proc from Kiril, Fury of Beasts is a somewhat complex thing to discover.  What I found is a little disappointing.

I have the normal polearm which, on proc, provides +107 agility buff once a sec to a stack count of ten and then persists for ten more seconds.  The LFR version provides a stacking +95 agility.  The heroic provides a stacking +120 agility.  With some modeling and a 45 sec ICD, I expected the normal to provide approximately an average of 365 agility in the best case scenario when averaged over the course of a whole five minute fight.

For the record, I expected the LFR version to provide 324 and the heroic version to provide an average of 410 agility.

That was very optimistic and simplistic modeling.  I was guessing I could get it to proc within the first second when it really only as a 15% chance to proc per shot.  Put another way, I was expecting to have some level of the buff (from one stack to ten stacks) for 44.67% of a five minute fight.

What I see in practice is quite different.  Below is a heroic Ultraxion and normal Gunship from last night.  I expected to see much much better buff numbers and uptime from Ultraxion.  I see only 27.9% and 31.7% overall uptime of any stack count.  In the below images, the green zones are when the buff is active (at increasing stack counts):

Given these observations I'm thinking my optimistic theory-crafting is supplanted by the observed data.  My average uptime is really only about 30% so my average agility for a fight is about 68% of my original calculations.  So the average agility gain from the proc would land around these:

LFR: 221
Regular: 249
Heroic: 279