I've fixed dozens of Klipsch speakers with glue issues from KLFs & Epics to KG 3.5 & 4.5s. Each and every time all I did was remove all the drivers, crossovers & wiring, dampening material and binding post plate. Then used a rubber mallet on the inside of the enclosure to loosen and remove the rattling culprit.
Once the rattling board is removed you take a 1/2" wood chisel or similar and proceed to remove all the old glue from the board you removed and from the enclosure. It comes out fairly easy and shouldn't take more than an hour to do both speakers.
After the glue has been removed is a perfect time to add any internal bracing for your cabinets to stiffen up any unwanted resonance or dampening material like Dynamat for your horns and woofer baskets to combat the same unwanted resonance if your so inclined.
Next step is to reglue the rattling piece that was removed. I always used liquid nail and never had any issues. I tend to use a bit more than less when applying my bead of liquid nail around the perimeter of the enclosure. Around the size of a #2 pencil will suffice but lean towards using more rather than less. The fit of the removed board was always snug and didn't leave more than a 16th of an inch on any side which didn't allow any of the liquid nail to squeeze out and mess up the outside look of the cabinet. Any excess of glue will squeeze out inside the box, you can either leave it the way it is and let it dry or you can put on some disposable gloves or whatever you choose to use and wipe down the bead of adhesive that was squeezed out of the channel after attaching the removed piece. I personally let the adhesive dry wherever it ended up.
After letting the adhesive set for the recommended time, 60 min if you decide to use the proper liquid nail variety, finish reassembling your speakers. Don't forget your dampening material and speaker polarities when hooking things back up.
All in all it really is quite simple to do with about 25 dollars worth of tools from harbor freight and some liquid nail from your favorite hardware store.
Phillips screwdriver ( to remove drivers ect.)
Tube of liquid nail
I hope this helps someone in the future fix some great sounding Klipsch speakers.