If you want to your company to provide the best customer support in whatever industry you are in, you should build your own tools and put them in the hands of your customer supporting personal.
Figure out what you want to be the best at and build your optimal solution for this specific purpose. Use and integrate with Commercial-Off-The-Shelf COTS tools for parts of the business which should be standardized or which cannot differentiate you from your competitors.
The technology which is available these days to produce custom solutions is extremely powerful and well established. Cloud services and providers together with open source technologies provide a application development platform which can be used to make what you want very quickly in a capacity which fits your requirements – no problem.
The decision about “Build vs. Buy” should not be about about “Time to Market”. If you want “Time to Market” standardize the way you build and bring products to the market. Take Amazon AWS as an example. It blows my mind, every time Amazon brings out a new service fully integrated into it’s product portfolio.
With the today’s changed technology landscape, the time which it takes to bring a custom solution into operation becomes limited by whether you can formulate what you want well enough to implement – not whether you can implement. Time to market of custom solutions is bounded not anymore by development time, but by requirement eliciting time.