I think the average here is rather dangerous - what I want to know is something completely different. What is the chance of it dropping off in twenty seconds? What is the chance of it dropping off in fifty seconds?
Chance the buff drops: (1 - chance to refresh) ^ (duration / time between chances) = (1 - .36) ^ 5 = 10.7% chance
Time to drop off = duration / chance to drop off = 93.13s
So you build it up for ~30s and after that it will stick for about 93s. (Let's say 90 to be safe and keep math easy)
270 sta for 90+ + ~135 for 30s over a total of 120s = 236.25 sta on average.
The 90s/120s also corresponds to the 75%ish uptime of the full stack.