This is EL here trying to help you get your answer. I pulled this from AR 601-280, the retention AR. I hope it helps. I would still ask your career counselor, there may be a loophole for you. I am just a retention NCO and not the expert.
4–9. Reasons for Extensions of Enlistment. Requests for extension of enlistment described in this regulation may be approved for the following reasons. Upon receipt of the approved DA Form 3340-R and verification of eligibility, the servicing Career Counselor will obtain an extension control number (ECN) from Commander, HRC, via the RETAIN system. The ECN will be entered on the soldier’s DA Form 1695. Extensions for purposes other than those listed in this paragraph will be evaluated by the soldier’s immediate commander, approved as outlined, and accomplished only when the soldier is within the reenlistment eligibility window and will not exceed a cumulative total of 12 months on any one enlistment, unless otherwise specified. Extensions are not authorized once the soldier is within 3 months of scheduled ETS, except when prior approval has been obtained from CG, HRC (TAPC-EPR).
a. Meeting SRRs. Extensions may be accomplished as prescribed in table 4-1. Soldiers within the reenlistment eligibility window and otherwise qualified, must reenlist to meet the SRR, they may not extend. Soldiers not otherwise qualified for reenlistment may be extended. Eligible soldiers who are not in the reenlistment window may extend or reenlist to meet a service remaining requirement. Soldiers who have extended their ETS to comply with service remaining requirements and subsequently request reenlistment because their SRB may be adversely affected by a later reenlistment must be properly counseled on the effects. Soldiers should be advised at the time they request an extension, especially if they are currently eligible for an SRB, that the extension will count as previously obligated service even if the extension is canceled for the purpose of immediate reenlistment. (Pol Msg 00-03, 9 NOV 99)
b. Retirement. AR 635-200*, chapter 12, applies. Soldiers applying for retirement may be extended through the last day of the retirement month. DA Form 1695 (Oath of Extension) is not required. The retirement order will serve as documentary evidence of the approved extension. Extension Control Numbers (ECN) are not required for retirement extensions executed according to AR 635-200*.