In my application, your first guess - with the
downstream C and some "sharpening back up"
you have a current-controlled delay stage
(one-sided - the HL is not strongly affected
except by the drive-strength balance moving
effective inverter DC threshold, the LH can
go from "2 Rds in series" to "open").
I use a "sniffer" bias circuit on a pad, where the
user can hang a set-resistor, to develop user
settable nonoverlap timing in a gate driver.
Force a voltage, take the current, bounce it
back onto the inverter Vdd, badda-bing.