You can open a JPEG as many times as you like and close it again without increasing the artefacting; they only degrade when you make any change and save.
I've no idea what level 12 is (Spinal Tap's amp only went up to 11, so must be impressive )
But as long as you save the JPEG using the maximum quality/minimum compression, and don't keep saving/editing it thereafter, it should not get any worse. If you have to do something different for each agency, then yes, make a base TIFF version and use that to generate each JPEG.