i put an Adams Arms piston kit on a Faxon 16" 7.62x39 mid-gas-length barrel (govt profile, 1:8T).  The Faxon gas port was .089" to start with which works great for DI, but for piston, it would eject the spent brass, but the BCG didn't travel far back enough to pick up the next round.  3oz buffer, standard M4 CS buffer spring.

drilled the barrel gas port (drill press, very carefully) with #38 drill (.101") which yields a 29% increase in port cross sectional area (CSA), and bolt would only travel far enough back to lock on the mag follower, not the bolt catch.  Drilled to 1/8" (53% increase in CSA over #38), and got reliable next-round chambering, but inconsistent LRBHO (still 3oz buffer).  i went up to 9/64" (.1406", 27% incr in CSA over 1/8"), and have reliable action now, and it works with the 4.1oz buffer which is what i was going for, with reliable LRBHO.  Wolf 123gr FMJ steel case.

then i sent the barrel out to be shortened to my preferred length, 14.5", pinned & welded M4-72 muzzle brake.  got it all back, reassembled, and WTF!   insufficient bolt travel, didn't pick up next round, no LRBHO.  i guess the dwell time got shortened enough to affect the action.  went back to 3oz buffer, and now had cycling, but still no LRBHO.

the orifice in the gas plug is 1/8".  Since the barrel gas port was already drilled out to 9/64, i think the gas plug is now the flow restriction.  that, and i didn't want to have to hammer out the doggone pins holding the gas block onto the barrel (not easy, not fun).  So i decided to drill out the gas plug, a #29 drill (.136") gives me an 18% increase in gas plug orifice CSA over 1/8".  well, i found out it's hardened, and so i had order some carbide bits.  i ordered a range of bits, not knowing where i'd end up.  The #29 sized hole enabled fully functioning, chambering & LRBHO, with the 3oz buffer.  But i want to use the 4.1oz buffer, so i used the 9/64" carbide bit, to give me another 7% increase in CSA over #29, and now i have consistent action and reliable LRBHO with 4.1oz buffer.

in case you're wondering the OD of the gas plug is .310", so with 1/8" hole, the wall thickness is .093", with 9/64" the wall thickness is .085".  The hole on the bottom of the gas block that mates to the barrel gas port is #22 drill (.157").

I went thru this,exact delema. I used a midlength with an AA piston. Now AA says this is not an app they designed for as the x39 is such a low pressure cartridge and is generally better sampled at the pistol or carbine length.
I went thru the gas port diameters EXACTLY like you did. I settled on .125" just like the AK.
I also used the AA skeletonized bc.
As for the recoil system i used an LWRCI spring and piston. The spring can be shortened to desired resistance.
Lastly i worked all the CP mags for smooth ammo feeding. I also opened up the feed ramps reducing the 6 oclock barrel extention lug to 50-60%.
That rifle runs walmart tula reliably and has more restricted settings used for higher pressure ammo.
Currently using an SWFA 1-4x optic with tula ammo. Furthest i have shot it is 500 yards. Making chest hits is no problem.
This project is well worth the effort. Most of the guys that shoot my x39 have ofdered to buy it!