Wedge the trem and take all of them off. Use a 9 volt battery to block off the trem. You will be better off changing all the strings anyway (you said it was a while since you changed strings). Set all the fine tuners to the middle of their range before you put the new strings on.
Once you have the new strings on, bring everything up to pitch and take out the battery (or whatever else you are using to wedge it), and then check the tuning and bridge angle. If everything is looking good, lock down the nut, check the tuning and play for a while. Depending how things are at this point, you might have to open the nut and adjust some strings. Any that you need to do this with, set the fine tuner back to the middle before you tune using the machine heads.
The other problem you might have is that once you lock the strings at the nut, then you can't get them in tune at the fine tuners. If this happens, open the nut, set the fine tune to the centre, and tune either high or low (depending on where you were after locking the nut, you will probably be too high, so need to tune down a bit).
I have one to set up this weekend, but mine is worse - I have to fit the neck and nut before I start!