This sounds like it could be a huge waste of time compared to investing in other areas of the product. How have you determined that your customers care where your service is hosted?
In "MVP" testing, I found that one of the critical problems with the service was latency. Amatino was used as the data layer for a GUI accounting application. When the service was running ~200ms+ away, the application spent too much time doing 'loading spinners' and the user experience began to suffer.
This experience led me to adopt a distributed design, that allows Amatino to sit as close as possible to end users.
Fortunately, deploying to a new region is as simple as running one script, the process is fully automated. So I don't have to worry about trading time on investing in other areas of the product.