Hi David,
Did you ever get this sorted out?
If not here is another suggestion you might try. I have to warn you though, I've been told that this is an incredibly stupid idea, but I've always done it on my own guitars and I swear it helps.
Locking a non-locking whammy bar
Locking whammies (I'm trying to avoid saying trem, so please excuse me if I slip) have a mechanism that stops the string from moving at the sadle when the bar is depressed. If you don't have a locking whammy, the only thing that stops the strings from moving back up into the sustain block is the bend in the string. This does little to stop the string from sliding up the interior of the block as is evident by the stings no going as slack as they do on a locking unit (which is the locking units inherant problem, they pitch down and then go blahhhhhh).
Inside the block, the string block can be tapered, or it may have steps (two different sized holes that create an internal ridge). In some cases there may be burs or other defects inside the hole that 'catch' the string ball end when it slackens and prevents it from returning to pitch. If you have pinging in your bridge and you have ruled out the sadles and pivots, this may be what you are hearing.
Locking a non-locking whammy is easy. plug something in the holes after you install strings to prevent them from going slack. I've used modified accoustic bridge pins, pieces made of wood and even moulded silicone plugs. You just need to be careful that whatever you shove in there can be taken out if you break a string.
Anyone reading this rolling on the floor?