Your RSU agreements state your terms and rights. Any decent RSU agreement should require that you will sign a lock-up or whatever agreement necessary for the company's funding. I have no idea what you signed and what terms those include, so all we can do is guess.
You are free to ask for whatever, and they are free to say no. Your rights are by agreement and that is what needs to be reviewed and understood
This answer is for informational purposes only and is not legal advice regarding your question and does not establish an attorney-client relationship.
Allowing a business attorney to review any agreements you signed in relation to the RSU's may prove to be beneficial to you.
Louis T. Wierenga Assisting in mitigating your business and tax risks. www.LTWLAW.com E Ltw@LtwLaw.com Twitter @LTWLAW The information provided is for general purposes only and should not be construed to be formal legal advice nor the formation of a lawyer/client relationship.
Consult with an attorney to talk details and options. There is much to your question that cannot be addressed on this forum. I agree with my colleagues, the answer will likely depend on the agreements that have been signed. Best of luck!