First of all, I'm not saying that using a block when you tune up is going to help your problem, I'm just trying to get an idea of what you have been doing, I take it that from what you are saying, that the bridge actually tilts when you use the fine tuners, and I assume this was never a problem before you switched string sizes, so my best guess is that you are either missing a spring or your springs are fairly weak and need replaced with something a little stronger......................