MEK will dissolve the Bostik adhesive JBL used to bind the cone assembly to the frame, including the spider. Paint it on the glue joint with an acid brush. It will take several "coats" and more than a few minutes for the solvent to work. A piece of 1/4" wooden dowel, sharpened to a wedge at one end, can be used to scrape at the glue and GENTLY pry the spider from the frame, once the adhesive is soft. Definitely do all this in a well ventilated space. Likewise, the dust domes on old JBLs can be removed without damaging them, or the cone, by softening the glue with MEK, using a similar process.
Once the cone assembly is removed, check the coil and form for obvious damage or lack of roundness. Clean the gap by wrapping some adhesive tape inside out on a thin piece of stiff flat plastic, such as half of a playing card, and working the adhesive tape around in the gap.
This is how we do it in our JBL authorized speaker shop. If your coils are damaged, or you have an accident with the cones that trashes them, you can send the woofers to us, or any other authorized JBL service center, where they can be restored to original operating condition by the installation of a JBL kit (yes, kits are still available for the 127A!).
Ton Garson
Aural Technology, Ashland, Or