What an absolute nightmare! New guitar that Iām looking at for a student. Ibanez RG470PB. She changed the strings from 9 to 10 and cannot re-tune it without the bridge coming all the way up. So I offered to help. Iāve watched a dozen ādo this trickā videos and found Floyd Roseās own instructions. Nothing seems to work, including the blocking of the trem whilst doing the initial tuning. What am I missing? No matter how I set the fine tuners before starting, how much I tighten or release the trem claw screws, once the strings are close, thereās not enough adjustment potential to get the thing in tune. The bridge always ends up rising. The guitar is 3 months old, so the trem springs cannot be stretched out already and the new strings have had a good stretch themselves. Iāve never worked with a FR before - and probably wonāt again! - but seriously, how hard can it be? Talk me though it like Iām 5 
Itās probably a problem of springs adjustment. Watch this video, maybe it helpsā¦
Thanks @JackPK I tried again. Broke two strings and the same thing happens - the bridge always ends up coming up, and tightening the claw screws even as far as they go does not compensate. Iāve tried loosening these as far as they go before starting, but the result is the same. I swear Iāve done everything the videos are telling me too, but nothing even comes close to getting this axe in tune 
I canāt help you with the FR, sorry. But Iām curious as to why you are breaking strings. In my experience a new string only breaks if it is tuned well beyond its in-tune tension.
It was when I tried to compensate by loosening the trem claw screws. A ātrickā from another video. Just snapped the high E and the G string together at the tuning pegs. Go figure - Iāve never had that happen in changing thousands of strings ā¦
This is the way https://youtu.be/tPUS9MgCB4g?si=Jaw3eyh2hEKMACFJ
If you watch the video, you see the guy uses a purpose-made block for the trem. I used a pack of playing cards, sliding extras in until it was a perfect fit. Worked like a charm.
I have recently been tossing up whether to buy an interesting Strat that I saw advertised. Always been a Tele player, but was curious to try out a Strat. Then I started finding out about all the issues with the trem (I have zero interest in using tremolo). I realise you can block it off in various ways, but the whole messy business has convinced me that a tele is really the instrument for me.
Iāve set up a Floyd Rose many times, so I can offer some hints that will work. Once youāve done it a few times youāll realize itās not that difficult (not meaning to sound condescending here).
Remember; any floating bridge is a matter of achieving balance - the pull of the springs in the back of the guitar needs to match (exactly) the pull of the strings. You put on heavier strings, they pull harder, the bridge tilts up. As you have observedā¦ .and it makes sense, right?
So, from this alone you know that youāll have to tighten the claw screws in the back of the guitar, when switching from 9 to 10s. If the claw cannot get any tighter, then you need to install another spring (with 10s I would use at least 3, and probably 4 springs).
Now, to make it easy to set the balance - do this. You want to initially over tighten the springs, so the bridge is pulled back. Donāt need a crazy amount of pull, but start where itās definitely too much. Then block off the bridge so it sits parallel to the body of the guitar. If there is a cavity in the guitar body, use something like a business card, or cardboard from a pack of stringsā¦ just make sure that despite the bridge being pulled back, itāll be stopped by this material and sit in the correct (approximately) parallel position.
Now youāve effectively converted the guitar to a ātemporary fixed bridgeā guitar.
Put on the strings, tune up. This should be as easy as any hard-tail guitarā¦ because the bridge is not moving! If, for some reason, it starts liftingā¦ then youāve not started out with enough pull from the springs.
Once the guitar is in tune, the strings stretched in, and NOT locked at the nutā¦ start releasing tension from the claws slowlyā¦ until the bridge lifts ever so slightly! Just enough that you can pull out the business card, because the bridge is no longer pressing hard against it.
Now the whole system in correctly in balance, and from now on itāll be easy to change strings one at a timeā¦ to the same string gauge.
Try it - seriously, this method cannot fail
Thanks @Kasper That makes sense now that Ive played around with the FR a bit. All the same, Iād rather not do it again anytime soon 
Itās super common around here to see people dismiss the trem bar or just block it off right away.
I donāt think thatās going to change anytime soon, but Iām still making it my life mission to stand up for the trem bar 
Itās one of the most expressive tools on the guitar. To me, dismissing it is like dismissing bends or finger vibrato. Iād be really hesitant to play a live gig without a bar ā I use it all the time.
I just wish more people would experiment with it and be a little less afraid of it.