If the NASA employees want to work on this project, then NASA should be selling their experience to the private firms who want to develop this for cheaper.
It's not just private entities in the US that are interested in rockets and satellite deployments. (We're well on our way to four parallel GPS systems, after all. The US GPS, the European Galileo, Russian GLONASS and the Chinese Beidou system that are all coming online.)
And beyond GPS satellites and as Herr von Braun and others showed many years ago, rockets are dual-use technologies.