Aha! So someone else has experienced this ... and yes, the POP can be startling. I thought I'd broken the darned thing when it happened the first time. It ALWAYS happens when I change strings, and because I have acidic sweat, I usually trash a set of strings after a few hours using the Variax. Probably why I don't use that guitar a lot, although pure nickel strings and "Ax Wipes" do help prolong string life for me.
Just for the record, one time the bridge popped, and I lost one of the little hex adjustment screws from one of the digital bridge pickups. I heard it, rather than saw it, but gave up trying to find something that small. This is a design flaw in the JTV-69, in my opinion. That, the "ghost notes" issue, the lack of noiseless mags, and the battery drain problems are things that Line 6 is hopefully addressing for future versions.
Aside from not changing all strings at the same time, which I like to do for the same reason that you do (oiling the fretboard), maybe someone has come up with some way to help the claws to keep the strem assembly in place - that's the kind of know-how I'm looking for.
I'm curious about the noiseless pickups - did you have to modify the guitar at all to get the noiseless pups in place?
I got my 69S in October 2012, and have the same experience as Larry. I read a couple of posts before the meltdown of the spammers hitting the prior forum, but really not many complaints about this issue.
My 69S is my 2nd JTV -- got my 59 in May 2011, and have not had any issues with string changing like I've read recently on this forum... I did not install any extra stuff on the trem spring arrangement, but did change my pickups to DiMarzio noiseless. I usually dress and oil the rosewood fingerboard on the 59 and now the 69S when changing strings, and have all the strings off. When I did this the 1st time with the 69S, and took off the last string, the whole tremblock assembly was pulled away from the 2 posts and popped back to the body. It did it with a lot of force, and I was afraid it damaged the gold finish, but luckily it didn't. My '78 Strat has the standard Fender tremblock with 6-screws on the front of the assembly that hold everything in place, so this was new behaviour fo me, and it startled me.
You need about three hands to get the trem into position, put the string in the locking tuner, and get the string to lock into the slot at the bridge, wind it up enough to hold. I don't let go of the bridge until I have 2 strings (high & low E's) on with enough tension to hold the bridge. I use the trem arm to have enought leverage to hold until the 2 strings will hold it in place.
Now, I avoid removing all strings at once, I leave the outside high & low E strings on when doing a re-string -- the fretboard oiling works "ok" with this arrangement, but any dressing will need all strings off, so I put it off as long as possible, due to the hassle. I am not really a tremolo user -- more of a hand vibrato guy, and never used mine on the strat either. I put all 5 springs on my strat and back the trem to the body - improves sustain. Wish I could lock down the 69S's trem, but I tightened the spring claw and took it down to rest on the body, but I know it wil disengage from the pins the next time I take all strings off at once.
The tension of the springs has enough force to tip the bridge backards and up to pull away from the top flange of the pins and pop back on the guitar top. I took out all trem springs, and the bridge just flops around in the cavity -- it would need the springs to hold it in place, if it wouldn't disengage from the pins. If the 2 pins had somewhat larger caps on them, they would most likely be able to prevent the bridge from popping away... I notice the pins can be adjusted up & down (screwed in & out), but have not messed with that as I am unfamiliar with any bad effects this could give me...
I have an "acceptable" work-around, but don't particularly like it. I love my 69S (especially with noiseless PU's), and this is more of an annoyance, but would like to see if anyone has a solution that I'm missing. I am surprised this doesn't come up more, as it is quite a startling POP when it happens the first time -- so you want to avoid it.