I am in the same boat. Looks like there is the possibility of reinstatement if they accept the reasoning behind the lapse of the status. I am not sure though.
http://www.chhetrylaw.com/recent_activities.php?precent_activities_Id=20
4.7 Can a student with TPS and lapsed F-1 status apply for reinstatement to F-1 student status?
Yes, current regulations permit a student who falls out of student status to apply for reinstatement. See 8 CFR 214.2(f)(16). For example, this provision would apply to a student who worked on a TPS-related EAD or dropped his or her course load before publication of this FRN, and therefore fell out of student status. The student must satisfy the criteria set forth in the student status reinstatement regulations.
https://www.nafsa.org/_/file/_/amresource/8cfr2142f.htm
(16) Reinstatement to student status --
8 CFR 214.2(f)(16)(i)
(i) General. The district director may consider reinstating a student who makes a request for reinstatement on Form I-539, Application to Extend/Change Nonimmigrant Status, accompanied by a properly completed SEVIS Form I-20 indicating the DSO's recommendation for reinstatement (or a properly completed Form I-20A-B issued prior to January 30, 2003, from the school the student is attending or intends to attend prior to August 1, 2003). The district director may consider granting the request if the student:
8 CFR 214.2(f)(16)(i)(A)
(A) Has not been out of status for more than 5 months at the time of filing the request for reinstatement (or demonstrates that the failure to file within the 5 month period was the result of exceptional circumstances and that the student filed the request for reinstatement as promptly as possible under these exceptional circumstances);
8 CFR 214.2(f)(16)(i)(B)
(B) Does not have a record of repeated or willful violations of Service regulations;
8 CFR 214.2(f)(16)(i)(C)
(C) Is currently pursuing, or intending to pursue, a full course of study in the immediate future at the school which issued the Form I-20;
8 CFR 214.2(f)(16)(i)(D)
(D) Has not engaged in unauthorized employment;
8 CFR 214.2(f)(16)(i)(E)
(E) Is not deportable on any ground other than section 237(a)(1)(B) or (C)(i) of the Act; and
8 CFR 214.2(f)(16)(i)(F)
(F) Establishes to the satisfaction of the Service, by a detailed showing, either that:
8 CFR 214.2(f)(16)(i)(F)(1)
(1) The violation of status resulted from circumstances beyond the student's control. Such circumstances might include serious injury or illness, closure of the institution, a natural disaster, or inadvertence, oversight, or neglect on the part of the DSO, but do not include instances where a pattern of repeated violations or where a willful failure on the part of the student resulted in the need for reinstatement; or
8 CFR 214.2(f)(16)(i)(F)(2)
(2) The violation relates to a reduction in the student's course load that would have been within a DSO's power to authorize, and that failure to approve reinstatement would result in extreme hardship to the student.
8 CFR 214.2(f)(16)(ii)
(ii) Decision. If the Service reinstates the student, the Service shall endorse the student's copy of Form I-20 to indicate the student has been reinstated and return the form to the student. If the Form I-20 is from a non-SEVIS school, the school copy will be forwarded to the school. If the Form I-20 is from a SEVIS school, the adjudicating officer will update SEVIS to reflect the Service's decision. In either case, if the Service does not reinstate the student, the student may not appeal that decision.