Apologies if this is now out of context but have not read entire thread.
I am responsible for an extremely busy Telecoms Tech support desk (1st, 2nd line support and some 3rd line). It is a fine balance between getting calls answered and providing superb customer service.
However, I do not believe you should cap calls to a set time (e.g 10mins). Customers expect to have to wait to get through to support but will understand if it takes time to resolve the problem.
I personally have talked someone through completely reprogramming a crashed system in a call centre - the single call lasted just over 4 hours. In fact during that time I had to explain to the caller I was putting them on hold whilst I went to the loo!!
Yes, a superb level of customer service and an extremely grateful customer but people were struggling to get through.
At the end of the day you can only follow your companies policies
JB