Yes, I fixed it, I even went to far as copying out the raws and wanting to post them here, but then I noticed that the fix would only work within Masterwork, so I stopped.
You make a second reaction that accepts NONE:NONE:NONE:NONE with a reaction class, and add the reaction class to a copy of the skin template, and make the leatherwing bats use this new skin instead of the old skin to make leather.
This got me thinking whether replacing
[REAGENT:A:3:GLOB:NONE:NONE:NONE][REACTION_CLASS:SKIN][UNROTTEN]
[HAS_MATERIAL_REACTION_PRODUCT:TAN_MAT]
with
[REAGENT:A:3:NONE:NONE:NONE:NONE][REACTION_CLASS:SKIN][UNROTTEN]
[HAS_MATERIAL_REACTION_PRODUCT:TAN_MAT]
would work (I use 3 globs of skin per leather, should probably up it to 4 or 5 to stop fully-grown chickens from giving more than one)? Is the :GLOB: required for the basic sackhead modifications to work, for some reason? Since from your comment, I gather that the crucial part, in the end, is [REACTION_CLAS:SKIN] and [HAS_MATERIAL_REACTION_PRODUCT:TAN_MAT], stated in the reaction definition and the skin material template.
Also got me thinking about making a 2nd reaction (and a different material template that would probably mostly duplicate leather, for now) for tanning lizard/croc/dragon scales, currently I just set the scale material template with the same modifications as for skin, plus [MATERIAL_REACTION_PRODUCT:TAN_MAT:LOCAL_CREATURE_MAT:SCALE]
But yea, tl;dr: why is a 2nd reaction needed to tan leatherwing wing leather, instead of just removing the GLOB requirement from the sackhead modification?