One alternative is to enter your arbitration award as a judgment, then seek to amend the judgment against the owners of the suspended corporation. The process to amend will be fact specific. You are not the insured and have no rights against any insurance company. It is the principal's right to demand indemnification from any insurance available to the principal.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
Assuming your arbitration award has been converted into a judgment, this is simply a question of judgment enforcement. A suspended corporation is prohibited under California law from defending itself under most circumstances. Regardless, you may need an attorney to conduct a debtor's exam, or take other measures, to ensure that the assets of the corporation are not transferred prior to enforcement of your judgment. Don't wait to act on this one.