Claim: Transpose at 6 or more stars.
Justification: Enhancement bonuses from hats depend only on the current star force count, so whatever star the item transposes at essentially has the effect of applying that same level of star force enhancement bonus twice on the SW hat. So there are two cases:

• if the item being transposed has less than 6 stars, then the fully enhanced SW hat is receiving the +2 stat bonus a total of 6 times, and the +3 stat bonus for a total of 10 times (42 total stat).
• if the item being transposed has more than 5 stars, then the fully enhanced SW hat is receiving the +2 stat bonus a total of 5 times, and the +3 stat bonus for a total of 11 times (43 total stat).

Claim: Transpose at 1 star.
Justification: Write-up can be found here.

*Above average equips should be used whenever possible.

Thanks to Fearcely for this note and for pointing out that it's worth paying attention to when things are being transposed.