What would cause this kind of amplitude interference on my ADC recording?
This is not a very detailed answer.

It looks as if you are getting multiple echoes back from your target, where the phases between the echos are varying slowly. Sometimes they cancel each other out, sometimes they don't.

It's difficult to tell why this happen in a real setup but not in your test setup. Maybe your test setup does not accurately reflect the real situation.

I think you need to add even more information about your target (what you're measuring, what kind of speeds it's moving at) if you want more ideas.