Sounds about right. I wouldn't gate-out anything that would actually be there when in use, if you want to know what's going to happen when it's in use. I guess you could gate out all but one reflection at a time and do that separately for all of the relevant reflections, or just plot everything if nothing is coincident in time.
But what sort of signals will it normally be used with?
For the time-offset reflections, you might have to try to calculate the phase relationships of theoretical sinusoids for each frequency of interest and somehow sum, or otherwise account for, the offset (in time) reflections, vectorially. Do you have access to a network analyzer? That would be much easier. Otherwise, why not just use sines from a spec an's tracking generator, and maybe (slowly?) sweep the frequency, or, if no tracking generator, use a sig gen and step-sweep with one step for each spec-an measurement sweep? If you only have one or a few frequencies of interest, I guess you could just use a sig gen and a scope.
That's all just off the top of my head. You would need to think it through and make sure you were getting measurements that were what you need, and were valid. My point was that it might be easier to make sense of sine measurements, in the frequency domain, since there are additional reflections etc. But if it will normally be used with pulses, then it might make sense to characterize it with those, in the time domain.