First super-nerdy question: where do equipment retention rules live for HALO/HAHO jumps?
#1. For US ARSOF units and some rare Conventional Force Airborne elements that conduct MFF: United States Army Special Operations Command (USASOC) Regulation 350-2 (Training Airborne Operations) and FM 31-19, Military Free Fall Operations. USASOC has Proponency for the Army... and I believe for USN/USAF MFF elements as well. USMC? Hell if I know.
Is there a document, (see #1 above).
or does a jump master get final say?
#2. The JM gets the final say (IAW regulations and final decision from the mission's Primary JM and Airborne Commander). The Airborne Commander has a lot of latitude to approve/change things on the fly in an actual combat jump. Otherwise, for training jumps, the bibles are 350-2 & FM 31-19. Even unit SOPs have to comply with those documents.
If specific COTS gear is desired for employment & purchase by units, the items must generally be boarded/evaluated for approved usage. In other words, nobody at unit level is going to approve your using Gucci commercial gear unless it can be intelligently argued that it already meets the letter of the regulations. Kinda like the perennial question of whether a given boot is authorized for wear under 670-1.
If the reg is broad & general in wording... and doesn't specifically prohibit an item, that reg can often be generously flexed to allow things that function/look similar to already approved items. For instance... if the reg merely says that personal ammo pouches will feature a positive closure system and be additionally taped or banded down for the jump... then you can get away with most anything. If the reg says only pouch "X", "Y", or "Z"... then only X,Y, or Z are authorized.
I have no idea what the current versions say (2017 latest editions I believe), but ARSOF units (SF, 75th Rangers, etc.) have been issuing bungi shingles for years. I jumped all kinds of ammo pouches across the decades... and general guidance for load bearing gear was Big-Boy rules. Secure your shit, because if I have to stop training to perform a a lengthy DZ search for a sensitive item... one that flew away from your body/ruck upon opening shock... it's your ass. BTDT.
Can you do a freefall jump with Esstac KYWI pouches, stock or modified, and if the latter, what mods are needed?
If you are military and on MFF status... go see your Team Sergeant/Platoon Sergeant (first stop before seeing anyone else)... then your Bn Air NCO. Read the regs before you entertain them with your request. They'll get you that final decision. As to approved mods for that particular pouch, I've no idea.
In the world of command Responsibility and Regulations... the reg wins. In the real world of I need to do this shit right now... exceptions are made. I've jumped a Walther MPK folding stock 9mm SMG strapped below my reserve. There was no Army reg that said that particular weapon was approved for jumping exposed in that manner. But there were ancient regs that described jumping exposed weapons or filled kit bags in that position (probably left over from WWII/Korean Eras). So... it was a Go with the JMs who JMPI'ed me.
Bottom line, ask the question long before you need to jump. In a pinch, you'd just put the rig into your ruck, kit bag, or weapons container and jump it that way. Don it after you hit the ground and get out of your harness.
I'm not an MFF guy (done a little civilian sky diving). Just a long time Static JM ('79 - '11). But I'd not trust a single bungi closure (by itself) on even a Static Line drop.
Hope some of the above helps with your question...