Ozopart,
I would throw in that you're overthinking things a little

. I appreciate your approach of change one thing at a time and this does make a good reason to start by blocking the trem, or as you did, using a plastic (CC) shim to support it.
So rather than think of a lot of variables, I'd suggest this order of operations (worked for me, first try, granted I'd already done some of this when I swapped a neck with a 16" fretboard radius for the original in my fender.
1. Get your trem in about the playing position you want to use it. This means both height reasonable close to the action you want, and angle where you want it. do not worry at this point about if it's in tune, but strings not loose nor set above normal tension (they can break of course).
2. set string heights / action using the very small hex screws in the saddles, you're wanting to match the radius of the fretboard (strings 3,4 highest, 1,6 lowest. I like a pretty low action and don't often push my strings hard, so long as you're not buzzing against the frets when you pluck at 11, you're good.
If you can't get the action right on all strings, go back to step one and adjust the two bridge-pivot screws. All things considered you don't want to be jacking the saddles up high, if 1 & 6 are lifted very far off the bridge baseplate, then you probably want to increase the bridge plate higher.
3. set the intonation, this is adjusting the back screws of the bridge to make the string longer / shorter. This will affect tuning / tension, so you may want to adjust tuning at this point, but if you don't mind listening to off-key tones, it's not important If you want to use an electric tuner, then in-tune probably helps. Play a string fretted at the 12th fret and then play the harmonic at the 12th. The note should be the same.
If the fretted note is higher than the harmonic, the string needs to be lengthened -- tighten the saddle position screw a bit, if it's lower then loosen it to shorten the string.
You probably don't need to iterate between these 3 basic steps, but it's OK of you do.
Now that that's all done, you can make final adjustments to the tremolo spring tree and tuning to bring the bridge angle to exactly where you want it.
Lastly, if you change your strings to lighter or heavier, you will likely need to adjust the springs tree or even add / remove springs. Of course you may also need to adjust the neck truss-rod for if you do this, I din't *need* to when I switched up to Medium strings for a while on my Fender, but I did need to go from 2 tremolo springs to 3.