As an update, to anyone else with a similar problem. I ordered the solvent that I referred to and finally got around to trying it out to clean up the JBLs this past weekend. I had a shoulder injury shortly after the stuff arrived and had a feeling this would still require a certain amont of "elbow grease", which would have been impossible with one arm immobilized. So now a couple months later, after weeks of PT, and getting caught up on the work I'd missed, I'm nearly back to 100% and had to make time to get these done. (Because apparently you can't have Christmas with a pair of sticky JBL monitors and their flight cases, in the middle of the living room.)
The solvent arrived quickly. The guy won't win a lot of awards for packaging. You get a short wide-mouth glass jar with a piece of cling-wrap under the screw-on lid and a wrap of black electrical tape around the works. The wide-mouth jar is ideal for dipping without a big mess. The solvent itself is somewhat oily, but almost odorless, which was a nice surprise.
The instructions are clearly written. They suggest you use a paper towel dipped in the solvent, but not dripping wet, to apply a light coat. After that, it's just a matter of working it in and rubbing the gummy stuff off. In some extreme cases they recommended leaving the solvent sit overnight, but in most cases you just have to work. If I let an area sit longer with the solvent, it didn't seem to matter, so I just did one area at a time. For me, rolling the towel as I rubbed did the best job of lifting off the bulk, then I could take a lot less solvent and keep wiping the residue off the same area until it was all gone.
The most difficult part was getting the gummy stuff out of the little grooves that trace the outline of the tweeter waveguide and woofer. The solvent seems to make the polymer coating you're trying to remove turn whitish, or maybe it's the towels, so leaving it in the grooves wasn't an option. It looked terrible, so I had to find something to clean out the grooves. I had a couple old-fashioned cardstock pricetags, that happened to be in the box I was using to discard the spent paper towels. Those worked nicely in and around the grooves. The gum would roll up, and eventually roll out of the groove, or stick to the edge of the cardstock. Then I could cut a nice clean new edge on the tag with scissors and repeat until the crud was all out of the grooves.
The instructions warn you not to get solvent on the enamel paint white letters and numbers on the buttons and meters, and not to get any on the speaker components. They suggest wiping the solvent off with Windex if you do. The woofers in these things use a foam 'surround', so I'd hate to assume the solvent is safe with that specific type of foam. The problem is, it's hard to tell exactly where the formed curvy box ends and the speakers begin. So in addition to worrying about accidentally poking a hole through the 8", or denting the dome tweeter, now I was nervous about getting solvent on them too, but pressed on doing everything outside those grooves on both boxes. Despite my best efforts, I did lose a little white paint / lettering on the first one. The button labels and meter markings are almost gone in a couple places. No matter how careful you are, they're just too close together to avoid contacting with solvent. On the second one, I masked off the meter with tape, but there's not a lot you can do with the row of little round buttons other than be even more careful. So live and learn, there. You want to keep the gummy stuff from mucking up the buttons, so you have to get in there somehow.
So now a football game later, everything is cleaned up pretty nicely except the area inside the grooves, where things get dicey with the woofer and tweeter. Before I discovered this solvent, as I'd mentioned in a previous post, I was considering disassembling them and treating them with a more common commercial solvent. I've been cracking things open repairing them, and putting them back together since I was a kid, so I wasn't overly concerned about damaging anything in the process. As hard as you have to rub the gummy stuff to roll it off, there was just no way to get close enough to the drivers without ruining them, or depositing big gobs, of what would basically be an adhesive, around the edges. Maybe if you had a 10,000 cotton swabs and the patience of Job you might be able to roll it off a millimeter at a time. No thank you, hand me a screwdriver.
With the speaker lying face down, I removed the 6 large screws on the back that hold the heatsink / amp module / brain to the box. It is gasketed, so unless you want big ugly pry marks, or want to compromise the seal on your studio monitors, you have to find a way to break it loose with prying. The heatsink is cast, and the fins are deep enough that if you have a nice big screwdriver and the speaker now lying on its side, you can get enough leverage to pop the whole thing loose with very little force. Grabbing it with channel-lock pliers or vice-grips would surely do the job too, but might leave bite marks.
You get a tiny bit of leeway on the wiring harnesses, so this is where you have to go slowly and get a light in there so you can see what you're doing. One thin ribbon cable on the left rear of the PCB, three unique (can only fit one place, so no need to mark them) molex connectors on the lower right. You have to release the ribbon from its grip, and the molex all have a small locking mechanism. Then as you ease the entire thing out, there's one more inline molex connector wrapped in a sticky foam tape you have to release to disconnect from the speaker harness. 8 short bolts hold the woofer in the box, and 4 small screws hold the tweeter in place. All of them have a red waxy threadlock type goop on them. I pulled the spade connectors off the woofer, and left the rest of the speaker harness attached to the tweeter and set them aside. Caution, there's a thin rubber O-ring around part of the tweeter / waveguide you have to account for.
I worked the solvent around the rest of it and it was very easy without the drivers in there, so in hindsight, the whole process would have been easier had I disassembled them from the start.
I took some pictures along the way incase anyone is considering doing it.
The solvent works. And they recommend when you're done with a surface, going over everything with Windex a few times, which did shine things up nicely. (and maybe neutralizes the solvent?) You might have been able to accomplish the same thing without any chemicals, or a cheaper goo remover, but I went with something specifically suited for the job, no regrets. Had I disassembled them first, I might have been more liberal with the solvent, but after I was finished, I see I got the job done using maybe 1/20th the amount in the jar. I'd barely made a dent and probably have enough left to do 40 more. After several hours and half a roll of paper towels, the solvent still only had a very faint oily smell. This time of year, without any fresh outside air, that was a pleasant surprise.
The big decision someone else might have, is whether or not they're confident enough / skilled enough to disassemble (and reassemble) fairly expensive speakers on their own. Tool-wise, it took 2 phillips head screwdrivers,( 1 large and 1 small) plus 1 flathead screwdriver for releasing the ribbon connector. Had I known that to get the results I wanted, it was unavoidable - I would have been much better off taking them apart first.
I hope this is helpful to anyone else who stumbles across this thread in the future with the same sticky JBL problem.