analyze the effect of some new changes to business rules on customers retention and sales

I am trying to analyze the effect of a particular business rule on customer behavior.

Background: I have two call centers operating in my company. One is an in-house call center and the other one is a third party. The incoming calls are handled by these two call centers based on some rules. 2 months before we changed some operational rules after which all the calls will be routed to call center A and then if not attended to call center B. Call center A has been performing well initially, in the sense customers coming through call center A drive more sales and is retained more than call center B. Now, call center A has been getting more calls and the hypothesis is that customers have to wait in the queue for a long time which eventually affects our sales and retention. I am trying to analyze if there is any difference in the sales, and retention since the rule implemented. So what I am looking to do is Pre-dateXXX and Post-dateXXX sales and retention. I tried some visualization which shows some differences.
But I am not sure how to approach it statistically. There are two approaches I have been thinking of:

1. Build a logistic regression model and see the effect of this variable on the target variable (retention)
2. Take a sample of data from pre and post and do a Chi-square test on both to understand if there is any difference between call center A and B.

I am not sure if my approaches will actually solve the business problem: does the customer has to wait in queue for a longer time in service and how is affecting retention and sales data analysis?

How do I approach this? Can someone guide me?