I don't think so, the slowed for DoS is only on a hit. The 'weapon' entry is under hit and not 'effect; which would be hit or miss.
So SSS: on a hit does damage, slows and stops target shifting
DoS: does the same damage and slows only with the listed weapons (no stopping shifting)
I'm still not sure that you're right.
The rules on power descriptions don't tell us how to interpret the "weapon" entries in the Fighter powers: all we have is the brief remark on p 77, that "The choice of weapon you make also provides benefits to certain fighter powers."
So we have to go on the text of the powers. On a quick read through, nearly all of the Weapon entries either adjust attack rolls or crit ranges, and appear indented after the Attack entry, or adjust damage and appear indented after the Hit entry, or modify a condition imposed by a hit and appear indented after the Hit entry, or modify an Effect and appear indented after the Effect entry.
Dance of Steel seems to be unusual in that the Weapon text is not modifying damage, nor an existing consequence of a hit, nor an existing Effect (that is, there is no "Effect" entry for it to appear under).
So I don't think my reading is excluded by layout or labelling considerations. I don't think it makes the power overpowered (Sleep gives auto-slow vs multiple targets as a 1st level Daily). It makes the power different from, and (at least plausibly) better than Serpent Steel Strike.
Another power with a complicated Weapon entry is Rain of Blows, which some have read as overpowerd on the basis that it gives a secondary attack for each hit. If it is read in the same way as I am suggesting that Dance of Steel be read (namely, as an effect independent of a hit, but not qualifying an existing Effect entry) then it becomes non-overpowered.
So I think that there is good reason to prefer my reading of the rules.