Or maybe link an immunity to sleep/fatigue but give it a requirement to use (ie taking a breather)?

If you really wanted to do a 'take a breather' character in that you compact long rests into shorts via physical quickness you might also be able to accomplish this with linking regeneration but just limit it as above.

Or maybe giving yourself an 'Dynamic/alternate power' of physical quickness and explaining it as thus?

Been awhile so I dont know if this would actually work or not~ someone check my thoughts.