I've converted a fair amout of '06 to 6.5X55, there are different ways but the main thing is the order of operations, no the number necessarily.
First, knock back the shoulder, this works best in two steps (.358 Winchester size die with the expander out and backed off to put the shoulder/body junction in exactly the right place, then .308 Winchester to draw down the neck), then draw the neck down to 6.5mm (might want to go 7mm first, as in 7mm-08 or possibly 7x57 though the x57 die will be too long to go all the way), then FL size in a x55 die. You can trim after drawing the neck to .30, 7mm, or do it last.
Last thing is fire forming. The .473" case head needs to be swelled a bit and here is a trick I learned from 45 2.1: Cut a strip of cellophane tape about 1/8" wide and wrap it around the case just in front of the extractor groove so it centers the case in the chamber. Don't overlap the ends of the tape, make sure the tape is uniform thickness all around. Carefully slip the cartridges under the claw extractor (if a Mauser action) snd try not to rake off tje tape during chambering. If a push-feed, use your finger to push the cartridge home and run the bolt home to snap the extractor claw over the rim. This will prevent uneven case head expansion (and potentially dangerous guppy-ing) when fireforming.
Some say this conversion weakens the brass and it may, but I haven't had any problems yet doing it for reasonable load levels.