So, it woulds like you will be testing for frequency deviations or
'jitter' created by the ICs under test. If this is correct, and you
want to measure this linearly, then you can't use one microcontroller
and loop the signal in and out several times, because the outputs will
all be synchronised with the uC clock.

Yes, thats pretty much what I would like to do. Luckily I have extra
uCs so this should not be a problem. The frequency deviation is really
what I was trying to convey in the above post. This is for a
demonstration for people who won't necessarily know what a 'frequency
deviation' would be (uCs are will be like magic boxes to some people
reviewing this) so I have been using 'signal integrity' as a blanket
term for it, though I recognize that it is not the same thing.

So now it occurs to me that what I really need to do is use one uC to
generate the signal and send it to the IC, which sends it to another uC
whose internal clock will be determined by the incoming signal and then
output the signal, which outputs to another IC, and repeat over and
over.

My other issue is budget in that I can't do this project too
excessively, though I will recycle the components. So any expensive
equipment is out the window at this point.

Also, I am trying to recreate 'real world' conditions with this
project, so using things that are not necessarily used in consumer
electronic products would make this project moot.

Thanks, and if you still have some resources on ways to do this, I'd be
much appreciative.