Cost Effective Driving Distance API

I am working on building a tool that allows a user to upload their address and then find the driving distance from their address from a large list of other addresses (up to 300). I have a working demo of this tool, I utilized the OSMR API to get these driving distances but I am interested in how I would scale this in a production environment. I have looked into Google's Distance Matrix API but it is kind of expensive. I also looked into running my own OSMR server on aws but that would cost me about $600 a month from my calculations. Any recommendations?