Happy to help!
All the best with your move!
After doing a bit of research, it seems that you do need to be working at a company in order to apply for a Temporary Residence Card (TRC), which is valid for 1-3 years.
The TRC replaces the business visa, so as far as I understand you will need to apply for a TRC within the country. You will need to have a valid work permit (which you can only get through an employer) in order to apply for a TRC.
I would urge you to speak to the Vietman embassy in the United States, +1 202 861 0737 just to confirm.