On a FR guitar both the truss rod and the bridge spring are countering the string tension, together. So changing neck tension de-balances the floating bridge and you need to have things in tune to check the playability. So you're looking at the usual FR tuning pain in the ass stuff + the readjustment of springs because of the rod, all at once. It might take a two or three cycles to get there. Better approach is to split the job in half and block off the Floyd from moving.
A chip of wood that fits exactly between Floyd and the body and blocks the bridge in full neutral position - have this piece carved out by using measurements for a specific string set and tuning, it's really helpful to have around.
You should be able to take off the neck without removing the strings, lay the guitar down, grip on headstock and pull it slowly upwards and not away from the body. When adjusting rod, do small turns, like 1/8 of a circle at a time. When you're happy with the results, refloat the bridge and it should now be slightly offset from the level.
Also a bit maybe worth out writing here. If you have a good properly setup Floyd Rose, and you didn't change string tension but de-balanced the bridge by other means (such as rod) you should be able to retune your guitar by screwing or unscrewing the backplate that attaches the springs to the bridge, just take one small wind or unwind at both screws and repeat until you see the bridge back in level position.
What's your problem anyway, fret buzz?