Your problem is deeper than it might seem at the first glance. Apart from numbers, it involves a remarkable phenomenon, which was studied in detail only a few years ago in the paper Phys. Rev. Lett. 90, 248302 (2003).
Suppose the puck is an infinitely thin disc, and it is sent across the ice sliding and rotating. What will stop first, translational or rotational motion?
The answer is they will stop simultaneously, and this does not depend on the initial translational and angular velocities. The origin is the intrinsic friction-mediated coupling between rotation and sliding. If rotation is too fast for a given speed $v$, the translational friction will be very small. And vice versa, if rotation is too slow, the rotational deceleration is small. Thus, there exists a "magic" value of $\epsilon=v/R\omega$ towards which every initial condition is attracted. In the paper cited above this magic value was found to be approximately 0.653.
This value fully characterizes the asymptotic motion of the puck and allows you to calculate the friction force distribution, deceleration and finally the path (which is a straight line in this approximation). In fact, a part of that was already found in the paper cited above.
However, this concerns only an infinitely thin disc, for which the pressure distribution is equal everywhere under the puck. With a thick disc you have more pressure under the front part of the puck, which additionally complicates the problem (still, see some discussion in the paper).
Finally, if you change the shape of the pack (as you in fact did by taking a ring instead of a disc), the magic value of $\epsilon$ also changes. See another paper that discusses this: Phys. Rev. Lett. 95, 264303 (2005). See also this comment to this old paper on puck motion on the ice.