Since I have a little more time to write.
I refaomed eight Earthquake Audio speakers that I had originally purchased in '92. Great speakers except for the foam. Based on everything I watched on You Tube and read on speaker forums, I carefully removed the dust cap with an x-acto knife. Replacement caps are cheap and easy to install if you buy ones that are slightly larger than the originals. In this case, I wanted to keep the company logo.
Clean the old foam off before doing anything. You don't want it falling down into the magnetic gap if you have your dust cap removed. Then remove the cap. Shim. I would run a bead of Aileene's Tacky glue around the cone and carefully place the foam in it before letting it dry for 24 hours. Then I could glue the foam to the frame using the same glue and another 24 hours. I could remove the shims and test the woofer with an old amp I had laying around before I glued the dust cap back on. Repeat the same process on the next woofer.
About the glue. Most of the refoam sites will sell you their "special" glue. It's Aileene's. Nothing more. Take a look at some pictures from Reaction Audio's site -
http://reaction-audio.myshopify.com/products/312x-powered-subwoofer. Those are from the build house that supplies them with some high end subs. You can see the gold glue bottle in the background. Pierce Audio Products is the build house -
http://www.pierceaudioproducts.com/. Finally, I wouldn't recommend a glue without using it. Here's a slideshow of a custom sub I had built by PSI Car Audio. They supplied the recone kit per my specs and I just dropped it into the frame. You can see in the pictures where I have the same glue bottle.
http://s3.photobucket.com/user/rlj5242/slideshow/PSI%2012%20Sub I pound that sub with a 1,000 watt Powerbass digital amp every time I am in the car. Two years later, there is no sign of the glue failing.