Maybe a reply from someone who works in financial would be the best use of your time, but I will try to offer some useful thoughts from an efficiency perspective.
It looks like the central problem is taking too long to open an account, and underneath that there is a recognition that there are "standard deviations," and the question is can those be streamlined. And of course there are different kinds of products and different media (channels) to sell them.
Whenever I look at how many people would be needed to handle work, I look at what things they are expected to do, how long would each piece of the puzzle take, and what are the probable reasons it would take more than one stroke for one piece to be completed. I have found that the speed in customer service doesn't depend simply on the ability of a CSR but on the effectiveness of communications that are on the exterior of the customer service hub, ie, what was the launch campaign like, was it very SIMPLE, was the information correct and consistent everywhere the end customer looked to prevent lack of understanding. The thinner the communication that is beyond customer service's control, the greater the chances a CSR is going to be going uphill and will slow down.
There are different products, can these be weighted by complexity, so that you can create "tiers of expectation"? Would account x and y demand a standard of small grade time, then loans and credit demand a standard of grade A time, then investments and disputes, whatever seems "more complex" or "heavy" demand grade A time? Then would the channels used to communicate with your customer service hub impact the resolution/sell time to some degree. For instance, it might be easy to assume that chat or email constitute a streamlined method of communication, but I know that I found this method quite lengthy when I needed help with my ISP provider, it was ridiculous, I could have gotten to the heart of the matter faster in spoken form. If you were to do draw a process map of the products/time/channels, I think it is the time values with communication method that will probably make your map look very complicated. Paper sounds very slow, but it might have the clearest way of gathering data and completing work in many cases, I don't know.
I hope I am on to something when I talk about setting up standard expectations or at least mapping how long it is taking in reality and trying to compartmentalize them into different types. As you identify the things that create the "uphill battle" to your CSR in the different product silos and the different forms of communication (are these what you are calling "deviations"?), my hope is that there would be an opportunity to discover how the "uphill" effect can be combatted and eventually prevented. If there is a micro group within your overall macro group that are able to reach their finish line faster, and is there an opportunity for some of them to pick up where a different/slowed down group have left off? Could certain individuals become tactical accelerators of an activity and lessen the time spent? One of the ways I manage to keep momentum going in my environment is to ensure that we don't have a one person=one job structure. I have people rotate tasks or enlist support of available teammates on a regular basis. This has the effect of not only adding support to completing something on time, but it also allows people to switch gears mentally and stay fresh. Not sure if any of that would be feasible for you.
I hope at least some of the above rambling from someone not immersed in the same world as you was of some use to you. If not, please don't be afraid to discourage me :)