I=CdV/dt, no way around it. The "I" of interest being your
output stage maximum current-throw, if C is the external
load.
That input difference matters so much, indicates a gain
shortfall. Back end current must not be fully steered by
250mV simulus' applied input difference. Although there
could be input/feedback network related problems (like
an output strength insufficient to drive the feedback
leg, leading to some nonlinearities of gain vs drive or
network values) - have seen these even in higher current
OTAs before.