Since you are a smaller company, I assume you are not going to invest in a large voice of the customer solution from companies like Qualtrics, Totango, etc. It sounds like you are interested in thinking outside the box and finding something engineers will use. One thing I know is that engineers enjoy interactive reports that provide data behind the story. So my recommendation is to consider www.tableau.com.

As with every anything worthwhile, this isn't something you can buy and finish implementing in a few minutes. But you can connect Tableau to a massive variety of data sources (or build your own using Phyton.) If you want inspiration, visit their gallery of examples.

I can see you putting your chat and twitter results into a word map in Tableau to show what is top of mind for your customers. Regression analysis of your survey results may be very helpful for making decisions about future product dev. I don't work for Tableau but I do have a lot of practical experience implementing it for Customer Success programs. If you want to learn more, I'm happy to discuss on a call.