Are you confident using APIs?
One solution can be making a series of API calls to an external service (Google, Here, Geoapify; something similar to this address Data Standardization - #5 by bruno29a, but with a routing service). How many distances do you have to compute?
Another solution is to compute a linear distance and increase it by a factor (10-12%) to simulate real distance. Not the most precise, but quick and costless. It might be an option.
RB