From the schematic description it does not sound like the OP is using display multiplexing at all. He is simply driving a series of 7-segment registers off a series connected set of shift registers.

In his application he really only needs to shift the data from the internal memory storage locations out to the shift registers + displays when there has been a change to the display content. It can be simpler code design and implementation to simply setup a timer interrupt that periodically refreshes the display from the internal memory variables and shifts that data out to the shift registers. That way the mainline program code can simply manage the memory variables and input switch detection and let the timer interrupt take care of keeping the display up to date.

In this proposed case of using the timer interrupt to update the display there would be no need to run those updates any faster than necessary to keep up with changes to the display caused by the mainline code. One could certainly choose to use a greater than 120 Hz update but it would be unnecessary. A 12 Hz update would work just as well.

Michael Karas