Can I file for an exception to policy or is there any other AR that allows me to skip a ht and wt screening prior to ETS and terminal leave?

No, you don't have a leg to stand on. The exception to policy specifically calls out your situation as something that IS NOT sufficient for an exception*

Bottom line: You'll be enrolled in the ABCP and flagged.

The impact to you will likely be minimal. You'll separate from the military long before you'd reach the end of the ABCP and (likely) be separated for non-compliance (which is what you're looking to do anyways...)

You'll have to do more weigh-ins and might be on an alternate PT program, however it's only two months according to your timeline.

The biggest impact on you would be the flag.
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* Request exception per AR 600-9, para 3-17b.
b. The use of certain medications to treat an underlying medical or psychological disorder or the inability to perform all aerobic events may contribute to weight gain but are not considered sufficient justification for noncompliance with this regulation. Medical professionals should advise Soldiers taking medications that may contribute to weight gain, or Soldiers with temporary or permanent physical profiles that they are still required to meet the body fat standard established in the regulation; the Soldier may be referred to an appropriate specialist for nutrition and exercise counseling as indicated.

Why do you think that being flagged for ABCP will disrupt your transition process?

In AR 600-9, Commanders have the authority to direct a body fat assessment on any Soldier that they determine does not present a Soldierly appearance to ensure Soldier meets the screening table weight for his or her measured height.

The regulation is not used to prevent testing but to promote a professional appearance of a soldier. Below are the exemptions. It doesn't seem like you would meet one of the exemptions. To get an exemption of policy would take the approval authority who wrote the policy. Since the policy came from a four-star it would take a four star to exempt you. You should start preparing now to transition.

Exemptions
a. Soldiers assigned or attached to a Warrior Transition Unit or Community Based Warrior Transition Unit must meet the body fat standard. Soldiers with special considerations may request a temporary exception to policy. See paragraph 3 – 17.

b. The following Soldiers are exempt from the requirements of this regulation; however, they must maintain a Soldierly appearance:
(1) Soldiers with major limb loss. Major limb loss is defined as an amputation above the ankle or above the wrist, which includes full hand and/or full foot loss. It does not include partial hand, foot, fingers, or toes.
(2) Soldiers on established continued on active duty and/or continued on active Reserve status. See AR 635 – 40.
(3) Pregnant and postpartum Soldiers. See paragraph 3 – 15.
(4) Soldiers who have undergone prolonged hospitalization for 30 continuous days or greater. See paragraph 3 – 16.
(5) New recruits. These recruits, regardless of component, will have 6 months from entry to active service to meet the retention body fat standards established in this regulation. Failure to achieve retention body fat standards after 6 months of entry will result in Soldiers being flagged in accordance with AR 600 – 8 – 2 and enrolled in the ABCP. c. Soldiers that do not meet the criteria of paragraph 3–3b have the option to request a temporary exception to policy. See paragraph 3 – 17.

You can’t get a waiver, your situation would not warrant one. If you just want out then you should continue to Soldier as required until separation. The military is looking out for your mental and physical health, why do you not want to do your part? Be as healthy as possible when you separate should be your goal.

Height and Weight standards are inevitable. Nobody can out run the scale and/or tape measure. Even those who are getting out, not up for reenlistment, going through a Med Board or anything else is subject to Height/Weight Standards. But from what I have seen of Army regs going on ABCP is a year long process. Which won't effect you much considering you are planning to leave by the end of January.

April 1 is a LONG way away. You SAY you are getting out. But so did I. Many MANY times. Eventually, I did,... after more than 20 years. Even then, I planned on retiring right at 20, but ended up going 7 months past that.

Doing anything OTHER THAN barring and flagging you would be irresponsible.

And I am speaking from your position. I got severely depressed and put on 15 pounds in 3 months, and ended up taping over. And I was flagged for it, too.

If you get flagged when you do the HT/WT, then you're flagged. All that'll really do is keep you from possibly getting an ETS award. Being flagged will not stop your ETS process. However, be aware that Leave, whether regular or terminal, is still up to the Commander. Be prepared to not be able to take all the Leave days you're talking about.

But to answer your question, yes their are exemptions...but your situation wouldn't warrant being granted an ETP.

Don't get too excited. I'm just satirically pointing out there might be a chance for push back in defense. Currently there is NO work around. However, the SMA has disclosed he's working on such a policy:

However................... one must get a 540 on the ACFT to be exempt if the policy takes effect.

https://www.armytimes.com/news/your-army/2022/10/12/army-wont-change-weight-tables-after-body-composition-study-sma-says/#:~:text=%E2%80%9CIf%20you%20score%20540%20on%20the%20ACFT%2C%20you,elaborate%20on%20other%20changes%20to%20body%20fat%20measurement.