Can you escape from Dimensional Shackles as easily as by polymorphing?

The intent of Dimensional Shackles (which block all kinds of teleportation or interplanar travel on their victim) is clearly to prevent spellcasters from escaping.

But what happens if a Dimensional-Shackled spellcaster casts polymorph on himself (and then drops his concentration)? Is he then free from the Shackles and thus able to teleport away? Or are the Shackles somehow linked to him and will still be applied to him, still preventing him from teleporting/planeshifting/etc. until he actually escapes by succeeding on the DC 30 Strength check?