Just a retired PJ for about the past 18 years. Most of my medical waiver and personal reliability program waiver (PRP) experience is from an assignment on the HQ ACC Command Surgeons staff. I worked beside the Docs approving/disapproving aircrew medical and PRP waivers connected to medical maladies. Of course with 23 years as a PJ I'm aware of several waiver approvals and disapprovals for cardiac concerns.
Duane Hackney, a PJ of most renown is example of an individual unable to get a waiver for cardiac ailments needed to remain on aircrew, jump, and dive status, but obtained a waiver to remain in the service in other less physically demanding AFSCs (Security Police and subsequently Intel). He died one morning from a cardiac arrest during PT.
AF Flight medicine waiver policy does not consider cardiac blood vessel stent or bypass surgery waiver eligible for the flying class (I, II, III) physicals. The Marine physical (military diving) doesn't consider consider cardiac blood vessel stent or bypass surgery conditions that should be waivered either. Regardless the medical waiver request must disclose what expected benefits will result if granted (approved). The waiver request can be considered to be a risk management decision. Being considered is the risk of further injury or death in performance of duties, any permanent duty limitations and or restrictions, and if required involuntary classification (job placement) into another less physically demanding AFSC or medical separation is required.
Cardiac blood vessel stent or bypass surgery conditions would require HQ AF surgeons approval after the request was screened through your current MAJCOM's command surgeon. Context being is the Command Surgeon lacks the authority to approve. The MAJCOM's screening is to ensure all the needed medical examinations, tests, lab results are present and available to the approving/disapproving authority.
The Air Force Enlisted Classification Directory clearly and distinctly states award and retention of Pararescue AFSC requires current Class III Flight Physical certification as well as the physicals requires for parachuting and combat diver duties. The initial exam standards sort of establish what can and cannot be waivered once medically qualified to perform aircrew, parachutist (particularly MFF), and combat diver duties.
As you only mentioned parachutist medical waiver concerns I didn't consider you being a PJ or CCT in my initial response. This is why I focused on the Army's medical waiver policies for Infantry duties (TACP, Security Forces or Army Ranger or Army Special Forces).
A review of AR 40-501 lacks me finding clear policy guidance for medical waiver eligibility criteria after basic special qualifications identifier is obtained, primarily because to be infantry does not require the service member to be a parachutist or a combat diver. Being a US Army Ranger is being Infantry. Being US Army Special Forces is essentially also being Infantry as the award and retention of the 18 series MOSs does not require performing MFF or Combat diver duties. The context being the disqualifying medical condition imposes duty limitation of prohibited from perform or accomplishing parachutist or combat duties, but not core inherent duties of the MOS.
AR 40-501:
Waiver authority for Special Forces training, Special Forces Assessment and Selection (SFAS), survival, evasion, resistance, escape (SERE) training, Military Freefall (MFF), and Special Forces Combat Diving Qualification Course (CDQC) is the Commandant, U.S. Army John F. Kennedy Special Warfare Center and School (USAJFKSWCS). Waiver authority for the Airborne School is the Commandant, U.S. Army Infantry School in coordination with AHRC.
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(2) Special Forces/Ranger combat divers and MOS 00B divers must have a physical examination every 5 (five) years. The physical examination for divers must be performed by or reviewed by a DMO or a FS trained in diving medicine. The physical examination for MFF parachutists must be performed or reviewed by a FS every 5 years in conjunction with physiologic training.
I suggest you read paragraph 8-26. Cardiovascular Screening Program (CVSP) and 10-24. Cardiovascular Screening Program (AGR Soldiers) found in AR 40-501.
10-24. b. Soldiers who do not obtain CVSP clearance will be medically flagged and processed through the MMRB in accordance with AR 600-60.