I have a Snark that I use to tune a Mexican Fender Stratocaster. When I tune to drop D, all the other notes get out of tune as well, and it takes me 2 or 3 minutes longer to tune because the strings go out of tune as I tune the others. Is there any way to tune to and from drop D faster (without removing the floating bridge)?
You could consider something like the EVH D-Tuna. I think it will solve some of your problems although I don't know enough tech to know if you could install this specific system on your guitar.
The EVH D-Tuna is a unique patented device that enables players to drop the E to D and back, in an instant. D-Tuna has been standard equipment on Eddie Van Halen's personal guitars as well as signature series locking tremolo-equipped guitars since the early 90's. Since then thousands of D-Tuna's have been sold all over the world. D-Tuna is proud to be endorsed by many professional players such as Warren DeMartini (RATT), Michael Wilton (Queensryche) and Dave "The Snake" Sabo (Skid Row) just to name a few. Bottom line...It's simple to use and it works.
"It couldn't be easier to install. You remove the string locking screw from the low E-saddle on the bridge and replace it with one of the two D-Tuna locking screws, the spring assembly and the D-Tuna. And that's just about all there is to it." - Edward Van Halen
In a word, no. It's the nature of the beast. String tension acting against spring tension. As you've found, when the tension of one string changes, it affects the pitch of other strings. Almost a catch 22 situation, and a long levelling out process. By blocking the vib it solves most of the problem, but there's still a little settling of the neck to contend with, and strings re-bedding themselves.
For a lot of players, that extra guitar is the answer, already in its own tuning. Is is actually possible to have too many guitars...
Or - fit a dropping machine head, which is adjustable so that when the lever is flicked, it takes the bottom string to D, but there may still be a little fettling to do. Company brand - 'Hipshot'. I sometimes play with a guy who has one fitted to his bass, which doesn't seem to affect tunings of other strings, but it's a bass, with only 3 others, and it's hard to tell sometimes anyway...