Traces over ground plane
Generalizing, the best option is to minimize disruption to the ground plane and this means using the interconnection method between R1 and R3 as shown in your diagram.
Generalizing, the best option is to minimize disruption to the ground plane but, now that I understand what you are asking, I'd put power tracks onto the ground layer in preference to signals. Reason: Power tracks are usually DC or low frequency (and highly capacitively coupled to real GP) and can act reasonably well as a surrogate ground plane to signal tracks on the other layer.