Improving my impulse counter circuit
You are probably correct about why you're always seeing a "1" on the display on power up. As C3 is charging, the Schmitt Trigger U2A will see it as a low voltage until the voltage on C3 exceeds U2A's minimum threshold. With such a large value for R1, it takes a long time to charge up C3. I'm assuming the pendulum is relatively slow if you're using such a low frequency low-pass filter.

An elegant way to prevent that erroneous behavior is to put a similar low-pass filter on the ~CLR pin of U4. If you choose an RC time constant this is slightly larger than \$R1*C3\$, it'll guarantee that U4 will come out of reset only after U2A has stabilized.

The ~RBI feature is actually easier than I think you are thinking it is. If you just hard-wire it to ground, the chip will automatically blank the display for zeros, but illuminate normally for anything besides zero. In other words, you can get rid of U9 completely and just tie the pin to ground. You can see from the datasheet that if ~RBI is driven low AND all of the inputs are low, the display will be blanked. If any of the inputs are not low (a non-zero number), it doesn't matter what ~RBI is, it will actively display the number.