#1
Now the first thing I'm gonna say is, please actually provide help, rather than just telling me my bridge sucks. It's better than others I've played to be extremely honest. 

Now, I bought a Ibanez EGEN8 and it of course has a Edge III bridge. I use the whammy a lot like Herman Li does, and It works well for the most part, except if I dive, it drops out of tune a slight bit. It's not a terrible change like some others I've played, but it's enough that I can notice it next to my friend's double locking bridge. I had talked to a guy on youtube that has the EGEN18, which is the double locking and higher end model of mine, and he said on his Edge III's he had this issue until he changed springs. Then he said it worked fine. But I didn't want to make that call until I heard what others think. I haven't done any mods to the guitar whatsoever. The bridge is stock. The springs are stock. The bar is stock. I recently changed a string and the bridge is slightly angled back, but it's not bad. It's a very very slight angle, and I have no idea how to change it, so I haven't done anything with it, because if it ain't broke i figure i shouldn't fix it. And with that angle, I think it's working better than it ever has in the past to be entirely honest. So I highly doubt that's the issue, but the possibility is there. I am a trem abuser like Herman, so that might be an obvious reason already, but Herman uses that guitar live sometimes for a few songs, so I know it has the capability of staying in tune for sure with the trem. If he can do it on his, I can do it on mine, but I just need the know of how. If anyone has any ideas, including the spring changing one, please tell me, as this will help me a lot! Also, I know it's set up right, minus that angle thing because I had it set up by a professional.
#2
The bridge needs to be level with the plane of the body to work at its best. It isn't just an issue of tuning stability, The position of the bridge relative to the body affects action and intonation. You can readjust the action and intonation to somewhat compensate for this, but only up to the point where the bridge saddles run out of adjustment range. It's a lot easier to set the bridge to be level with the body because doing it that way gives you a solid frame of reference that allows you to adjust the bridge to the same level consistently. Doing it any other way makes it a lot more difficult to reproduce consistently.

Adjusting the bridge to lean backwards by default limits the amount you can pull back on the bar too. And for Herman Ri's style, you need all the pull-back range on the bridge that you can possibly get., so long as you don't start to break strings.

Like I said, there's nothing to stop you from setting up the bridge that way, but its definitely not desirable.

If I was you, I would fully stretch the strings in to an inch of their lives, set the bridge to be level with the body and experiment with different spring arrangements until you get the best compromise. You have nothing to lose in trying. I would also strongly suggest lubricating the knife edges with Vaseline to reduce friction (the Achilles heel of the Edge III) to give the bridge the best possible chance of staying in tune. If there are any burrs or dull areas on the knife edges, remove them with a file, resharpen the knife edges, lubricate them and hope for the best. If that doesn't work then you're pretty much SOL and it's time to buy a new bridge.
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And well yes, I'll enjoy the carpal tunnel and tendonitis, because trying to get one is clearly smarter than any word you have spoken thus far.