Outputting correct data on shift register with clocks tied from microcontroller
Ideally you want to load in 16 bits of data using the SCK, then output all 16 bits in parallel using the RCK. Binding SCK and RCK together makes normal shift / load operation neigh impossible. Normally OE/G is low so outputs are always ON. No need to turn off unless another 74LS585 pair would be driving the same 16 outputs

If all 16 outputs need to maintain state and then change state at the same time then a proper shift / load sequence must be done.

The idea of using an MPU properly is to reserve as many pins as required to get control of external hardware. This requires detailed planning up front so you assign mandatory functions first.

Excessive pins are much better than coming up short on mandatory control pins.

Just out of curiosity, how did you come up short a control pin on a 20 pin MPU? Were the rest of the pins already committed to existing hardware?