A Floyd can be really challenging, but when they settle in they are super stable, more tuning stable than any vintage guitar with a fixed bridge.
I just re-strung my 1998 MIJ Ibanez RG-7 (Licensed Floyd Rose Trem) with Heavy Core Dunlop 10-60 strings yesterday, getting back into my 7 string DGADGAD thing, which is actually dropped to CFGCFGC, and it took well over an hour to get it in tune and get the trem sitting flat like it's supposed to.
Maybe more like 2 hours, but I finally got it and was able to lock the nut and keep going with the fine tuners.
The TC Electronics tuner is a Godsend for this job, which is endless retuning.
By the time you get to the high E you can start on the low E again, rinse, repeat...