Remote reset circuit does not work
You're assuming your 5V supply goes immediately to zero when disconnected.  In reality, it will fall slowly as LEDs have some capacitance, and they stop conducting substantially once the voltage across them is below their rated forward voltage.

In addition, you have current from both the 10K and internal pullups which largely has to go through your 1K pulldown.  As a result, until the capacitor is charged, you have a voltage divider which will keep the voltage across the 1K higher than 0V.

I'd suggest putting the capacitor and a ~100K-1M resistor in parallel with one side to ground, and attaching the other side to the unused terminal on the switch.  The capacitor will discharge to 0V while the unit is powered, and when you remove power, you drain the +5V circuit to near 0V (depending on the LED capacitances) until the capacitor charges.  You may have to adjust the cap value.