Problem:  Yes, in simple cases one can discuss absolute rotation; in fact, with respect to what would a Kerr black hole rotate otherwise (ans: asymptotic spatial infinity). That argument points up that to define absolute rotation you have to go  to infinite distance, asymptotically.  Look at the confirmation of the Lense-Thirring effect using satellites recently, and in progress with Gravity Probe B.  Locally, you can define a "nonrotating" frame with your ring laser (why bother?  Use a couple of gyroscopes! Gyroscope technology came long before ring lasers.)  Anyway, this local frame you just found does not tie in to a nonrotating frame defined by distant stars, quasars, etc. So if you believe that one, you are stuck. If you do not believe that frame based on distant obects is the nonrotating one, you have to explain how stars and galaxies many thousands of light years away are all orchestrated to move as they seem to.