In the #7 circuit, if C6 is there for switch debouncing, it is not needed. The counter is held in Reset as long as the switch is pressed, and comes out of reset only after release. This means that you do not need any debouncing, since trailing edge bounce is so brief that it will look the same as a clean button release. Plus, a debounce period of less than 100 us isn't very effective.
Thus, delete C6.
If C6 is there as a power-on reset, then forget all of that.
BUT ...
Revisit R2. To hold two standard TTL (post #5) inputs below a logical low voltage threshold requires 500 ohms or less *per input*. This puts the max R1 value at approx 220 ohms (for 12% margin).
ak