Before revision:  Using a new fractional charging argument and fork-fences to guide the partitions , we improve the approximation ratio even more to 4. We hope that our ideas will lead to further progress towards a PTAS for MISR.
After revision:  Using a new fractional charging argument and fork-fences to guide the partitions , we improve our approximation ratio to 3. In particular, our partitioning uses more general fences that can be sequences of up to O(1) line segments each. This and our other new ideas may be useful for future work towards a PTAS for MISR.