I know! It's foolhardy to disagree with Keith on any technical matter! And it's also a risky proposition to do a DIY re-surround job the first time. But my very first go-round was better than a pair I had professionally re-done by an authorized JBL service center (though JBL does NOT sell factory re-surround kits, and does not recommend re-surrounding... they recommend a full re-cone instead).
I like to use a 30 cycle tone to keep the voice coil centered in the gap while the glue dries. I have a few tricks...
I remove as much of the old surround as I can through mechanical means. A lot of times it will just crumble off. Usually there's still a fair bit of residue left on the back of the cone (or front, if the surround attaches to the front of the cone). I like to use a AAA battery with alligator clips to lift the cone just enough to allow me better access to the back side. I disconnect it periodically (when not directly needing to access some bit) so as to avoid letting heat build up in the voice coil (just a precaution).
I've found that isopropyl alcohol on a cotton swab is very good at dissolving and removing this residue, at least on JBLs. Obviously you do NOT want to get the cone wet-- it's an exercise in care. But with patience, you can get the cone cleaned to a perfectly clear, flat surface. I like to inspect with a pen light before proceeding.
Apply the surround to the cone using the appropriate adhesive , smooth out ANY gaps or wrinkles. Again, the AAA battery and pen light comes in handy. Then I like to allow this to dry and set completely. Once it sets up, I run a bead of adhesive around the cone right at the roll to form a good seal.
Finally, apply adhesive to the frame and affix the other edge of the surround... again, NO GAPS, NO WRINKLES. Then apply the 30 Hz tone at modest level to center everything, and keep it centered while drying. Listen for voice coil rubs (scraping sounds) and if you hear any, stop the tone and adjust-- you've got something badly off-center. I check them periodically as they dry to make sure the vibrating of the tone doesn't cause them to come unstuck. Sometimes I add some light clamping-- little soft clips around the circumference.
Once it's good and dry, I apply the gasket parts over that.
My track record is perfect (knock wood!) so far.