Provable ROI for call center rest periods? Think you can help make life better for a nation of call center workers?

At a large insurance company, I used to work in the call center for both Auto Claims and then Homeowner Claims, before I was promoted on to other things.  It's a complicated and stressful position, where customers are already upset because they have just gotten in a car accident or their house just burned down.  

Call volume varies, but tends to be constant during many busy periods. As soon as you're done with one call, sometimes there's a lull, but usually another call is waiting.

The problem is that this leads to people taking a breather during "After Call Work," purposefully inflating their call time in order to catch a break from the stressful calls.

A potential solution, I've always wondered, is to pre-program an automatic break of no calls for X minutes after Y calls. (e.g. a 1 minute break after every 3 calls.)

My question is, would there be any scientific basis that could help justify a Return On Investment? Is a rest period worth the drain on phone coverage?  Or is it more beneficial to leave it up to the workers, to sacrifice their Average Handling Time at will to decompress at their own pace?
This is the paper you would want to read on this topic. The paper empirically compares four modes of managing interruptions. It is a great (and long) read so I'll try to summarize the bit for you:

There are thus four modes of managing interruptions:


Immediate interruptions. There is no management whatsoever. As soon there is a distracting stimulus/task, it has to be attended to. In your case, you could think of being in a conversation with one costumer and immediately being switched to another. You can already imagine this is not a very good one. 
Negotiated interruptions. You can decide all by yourself whether and when to attend to the interruptions. You could choose to finish a difficult part of one task and only attend to the interrupting task when that is done. 
Mediated interruptions. Some other metric decides when an interruption is deemed appropriate. A well known metric is workload, as measured by pupil dilation. To bigger you pupil is, the higher workload is. Interrupting would be best in low workload situations (Salvucci and Bogunovic,2010)). What you suggested, the cooldown time, is also a mediated system. 
Planned interruptions. Interruptions only come at moments you have planned. Though this may seem nice, in many situations, such as yours, this is not possible. Even if you could plan the moments, in dynamic environments you cannot predict the best moments. You could have an incredible high workload on one day, and have nothing to do on another. 


So which is best?

The results show that the best interruption management systems are a combination of negotiated and mediated management (believe me on this one, I do not want to discuss 20 pages of results here haha). Mediated management systems will determine the best moments of interruptions which is incredibly useful. However, if workload is very high for a longer period of time, the callers may be on hold for too long. 

The negotiated management of interruptions allows people to work as hard as they can/want. Some people perform better under pressure than others and may choose to wait for a shorter period of time. The downside, however, is the fact that people are bad at this. Some people stress themselves out and never wait (Asking for reference here) and some people wait to long and may get distracted by other things (Katidioti et al.,2014).

A combination would thus be best. Mediate the interruptions, but allow the employees to continue working when they want to. In you case, you could have a short mandatory pause duration and a suggested longer pause duration (or conversely, an maximum pause duration). You could then determine the duration of the pause based on the length of the last call(s) for instance. 

I hope this answers your question and if you have any questions just let me know. 

EDIT: The literature I described above mainly focuses on multitasking, while your question is about sequential tasking. Nevertheless I do believe the above can be generalized to your problem. The interruptions are now in fact the breaks. 

A final note, if people purposefully inflate there call time, this may be an indicator that workload is indeed too high. Talk with the people and ask what they think of the situation and what they think may be a good solution. When changing an interface/task/process, people accept the changes much more quickly if they are involved in the process (Asking for reference). 

References:

Daniel C. McFarlane (2002): Comparison of Four Primary Methods for Coordinating the Interruption of People in Human–Computer Interaction

Salvucci and Bogunovic (2012): Multitasking and Monotasking: The Effects of
Mental Workload on Deferred Task Interruptions

Katidioti and Taatgen (2014): CHOICE IN MULTITASKING: How delays in the primary task turn a rational into an irrational multitasker