How can I use EB-5 to maintain my legal U.S. work status?

You can file an I-526 petition, but you will have to wait for the I-526 petition to be approved. Once approved, then you can concentrate on the U.S. consulate process.

You cannot get PR until your wife fulfills the requirements under Conrad 30, but you can file and get a work permit when eligible to file the I-14. In the interim you may need to go on an H-4 without the ability to work if you want to stay here.

You can apply for EB-5, but it does not resolve the two-year home residence rule issue. She and you need a waiver in order to benefit from the EB-5 petition, which will take at least one year to get approved.

Just having an application for EB-5 does not in itself confer any status. I am not aware of any restrictions as to the EB-5 program as to your filing. I am not familiar with J-1 or J-2 restrictions; you should contact your local USCIS office and ask them for an opinion, preferably in writing from them.

The residency requirement waiver does not give you an extension of your stay or status. Under the Conrad 30 program, your wife will be transitioning from J-1 to H-1B with consent to work where HHS needs the doctors. However, your J-2 status also has a residency requirement that is separate and must be waived independently. Since EB-5 takes at least 15+ months for I-526 adjudication, it is highly unlikely that you will be approved for EB-5 even if you are able to file within this month. This means you will not be able to work after June 2016. As a doctor working in the Health Professional Shortage Area (HPSA), Medically Underserved Area (MUA), or Medically Underserved Population (MUP), your wife should have a good chance for the EB-2/National Interest Waiver category of obtaining the green card and then you as the spouse, however.