Is there any way to reduce it other than to reduce the value of R1??The output of the BC557 does not "go" low. Instead the BC557 simply turns off and lets the 10k resistor pull the voltage down if it can.
I suspect the output of the darlingtons has a load that has the voltage spike and is causing the little voltage spike to feed through to their bases.
The transistor inverter has a high output resistance. You do not show a supply voltage but your SIM shows around 15V which is fine for using some Cmos CD4069 inverters in parallel to make a low output resistance to feed the darlingtons.Is there any way to reduce it other than to reduce the value of R1??