Before we go any further, how about you quantify:
"fast" and "slow" sweep time for a C-V measurement
on normal equipment such as shown
minority carrier lifetime in bulk regions
transit time for your device structure, characteristic
switching time or 1/fmax for your device
"Fast" on a Kiethley is still glacial compared to any modern
transistor's performance, but not necessarily "slow" compared
to some of the longer-lived traps (I have seen sub-Hz RTN
on small SOI transistors)
Your C-V structure in the interests of measurement is going
to be so large that it will not show you the individual detraps
but what you see on the "slow" curve is the cascade of them -
like water being squeezed back out of a sponge, you don't
get it all if you don't wait (the "fast" curve).
Meanwhile in the bulk of the explicit device, in normal operation,
Niagara Falls.