First you need a testbench which will give you a proper
Vio measurement for one single run. Then MC analysis
is just setting up loops and storing T*V*P datapoints for
statistical treatment.
I expect this will have to be a transient analysis as you
can't do clocks in any other, the kickback noise can be a
real significant element (high Z sources bad, low Z sources
good, but what is real application?).
A classical op amp test loop can turn comparator chop
into a proxy (up-scaled for measurement, then attenuated
back down) feedback voltage. This runs slow. A filter, maybe
behavioral, and a vcvs might work out for you - what you
need is a converging series of feedback events closing the
loop, not necessarily full precision op amp detail including
its slowness.
If your need for accuracy is modest then a ramp from Vid(min)
to Vid(max) @ Vcm (cases) might be more time efficient. Need
ramp to be well slower than prop delay. But you don't need to
out-wait a DC precision op amp's compensation-as-delay at
least.
Now what LTSpice has for MC support, I have zero idea.
I'd bet that there's plenty about it on the LTSpice 'boards.
I've been using ngspice.