Adding layers of fabric, or any air barrier, would seem to be counter to air pruning. I would presume that any restriction of outer surface exposure of medium/soil to air will obviously restrict air pruning, what you want. The drier the medium/soil (at the sides where you want air pruning) the more air it contains, which is what you want. So theoretically, I'd presume there is no upside (less air pruning) for adding a fabric liner to a fabric pot.
If simply adding a liner did something desirable, wouldn't that be prominently marketed; wouldn't we already all know this (not have to ask about this)?
Otherwise, with your using 15 gallon pots, relatively large, being drier or even dry the first few inches shouldn't matter or make a difference. There's loads of media/soil inside--as long as you keep what's inside sufficiently moist.
Also, larger pots simply can't do as good a job air pruning, or rather the air pruning will be proportionately less effective. The ratio of outer air-exposed surface area, the functional air pruning surface area, to inner contents (media/soil volume) is much lower in larger vs. smaller pots (with a lot more media/context far from any air-exposed surface).
If I used fabric pots and wanted to upgrade what I had for more air pruning, I'd sew on an extension, make the pot taller, definitely avoid liners restricting air flow/access. For example, I use Air-Pots for their air pruning and wrap/strap an extra 1/2 Air-Pot onto another. I generally add 1/2 (lengthwise) of a no. 3 Air-Pot to another no. 3; and with 1 row lost to overlapping, I get near 50% more height, volume, and that much more air pruning. For no added floor space area (too valuable in my crowded tent), I go from ≤3 gallon to ≤4.5 gallons and end up with a height/diameter ratio about 3:1 vs. the usual approx. 2:1, which should further benefit root growth.
