You would need an independent basis for a visa. Have you got a relative or employer who is eligible and would be willing to petition for you? A USC or LPR spouse, or a USC adult child (21 or older), a USC parent (or LPR if you are single), or a USC sibling? Would your education and experience qualify you for an H1-B non-immigrant visa (but allows dual intent) or an employment based immigrant visa?
You are not eligible to adjust based on your current status, that is reserved for G1 and G2 only (among the G's). Asylum is not a possibility in that you are a government employee.
INA 101 (a)(15)
(G) (i) a designated principal resident representative of a foreign government recognized de jure by the United States, which foreign government is a member of an international organization entitled to enjoy privileges, exemptions, and immunities as an international organization under the International Organizations Immunities Act (59 Stat. 669) 22 U.S.C. 288, note, accredited resident members of the staff of such representatives, and members of his or their immediate family;
(ii) other accredited representatives of such a foreign government to such international organizations, and the members of their immediate families;
(iii) an alien able to qualify under (i) or (ii) above except for the fact that the government of which such alien is an accredited representative is not recognized de jure by the United States, or that the government of which he is an accredited representative is not a member of such international organization, and the members of his immediate family;
(iv) officers, or employees of such international organizations, and the members of their immediate families;
(v) attendants, servants, and personal employees of any such representative, officer, or employee, and the members of the immediate families of such attendants, servants, and personal employees;
8 CFR § 245.3 Adjustment of status under section 13 of the Act of September 11, 1957, as amended.
Any application for benefits under section 13 of the Act of September 11, 1957, as amended, must be filed on Form I–485 with the director having jurisdiction over the applicant's place of residence. The benefits under section 13 are limited to aliens who were admitted into the United States under section 101, paragraphs (a)(15)(A)(i), (a)(15)(A)(ii), (a)(15)(G)(i), or (a)(15)(G)(ii) of the Immigration and Nationality Act who performed diplomatic or semi-diplomatic duties and to their immediate families, and who establish that there are compelling reasons why the applicant or the member of the applicant's immediate family is unable to return to the country represented by the government which accredited the applicant and that adjustment of the applicant's status to that of an alien lawfully admitted for permanent residence would be in the national interest. Aliens whose duties were of a custodial, clerical, or menial nature, and members of their immediate families, are not eligible for benefits under section 13. In view of the annual limitation of 50 on the number of aliens whose status may be adjusted under section 13, any alien who is prima facie eligible for adjustment of status to that of a lawful permanent resident under another provision of law shall be advised to apply for adjustment pursuant to such other provision of law. An applicant for the benefits of section 13 shall not be subject to the labor certification requirement of section 212(a)(14) of the Immigration and Nationality Act. The applicant shall be notified of the decision and, if the application is denied, of the reasons for the denial and of the right to appeal under the provisions of part 103 of this chapter. Any applications pending with the Service before December 29, 1981 must be resubmitted to comply with the requirements of this section.
(Secs. 103, 245, of the Immigration and Nationality Act, as amended; 71 Stat. 642, as amended, sec. 17, Pub. L. 97–116, 95 Stat. 1619 (8 U.S.C. 1103, 1255, 1255b))
[47 FR 44238, Oct. 7, 1982, as amended at 59 FR 33905, July 1, 1994]