cheers mate, i've just had a look at it.
i'm not a professional mechanic but i can share what i did to my Stillen G3 intake to resolve the same problem you're experiencing.
Page references are based on the labels at the bottom of each page.
Apologies for the use of two units of measurements - i'm from Australia where using both is acceptable depending on the context.
The stock breather system has these features:
RHS - 13mm restrictor orifice is in the junction where the breather hose barb pokes into the accordion pipe.
LHS (USDM driver side) - no restrictor. It is 16mm throughout. 16mm is approximately 5/8".
Page 61: The breather hose has a 5/8" inner diameter. Therefore the outer diameter of the barb it connects to on the supercharger intake is approximately 5/8". The barb's ID would have to be smaller (by quite a bit in this case, as it appears to have quite thick walls).
No issue quite at this point, as it seems to match the OEM setup in terms of hose inner diameter and the inner diameter of the barb fittings.
Page 70: Describes how a tee is used to join both cylinder banks' breathers together, drawing fresh air from the single 5/8" ID hose.
Because of this, the intake of fresh air is restricted by half at this point, and i reckon this is the cause of the sagging idle/stuttering issues you guys have experienced.
On my Stillen CAI, i cut off the LHS breather barb which has an ID of 12.5mm. Welded on a barb with ID of 15.5mm and my idle is about as good as it was with the stock intake now. RHS is left as Stillen made it.
As a simple test, i'd suggest disconnecting the tee and using a straight joiner for the RHS bank. ie. isolate the LHS breather.
For the LHS breather, clamp on a suitable small pod filter. Go for a drive and see what happens. Then try the idle relearn procedure if theres no difference (can be done without scan tools).
Ideally the breathers should draw from after the MAF sensors as the ccv system does recycle the crankcase fumes and burns it up. The fresh air drawn in to replace the fumes should be metered to ensure correct AFRs. But for a quick test it shouldnt hurt. The GTM setup draws from a suitable location but i reckon if you run another 5/8" hose to a new extra barb, it should unchoke it