I tried this process this morning and it is probably doable but there is a lot of back end setup and conversions that you need to work through in Civil3D for this to be successful. Doable but requires knowledge into the inner workings of yet another software. The other issue is that depending on the program or the company, setups could be inconsistent from file to file, like you mention.
Maybe a tml could help with this. I need to start learning to code.