Thanks Weston, you pointed me in the right direction and I was able to find the var_dump() statements in some legacy code in our theme.
My mistake was just looking in the AMP template files, but I realized that some core theme files like functions.php (in our case, a file loaded by that file) also get loaded and looked in there until I found the problem.
Thanks for your help. Could it be coming from anywhere in our theme (say, functions.php)? I have a custom AMP theme made by using overrides in an /amp subdirectory of our theme folder. I checked there and removed all var_dump() statements but still seeing the issue.
My apologies! So sorry for the inconvenience. Maybe I should have used your plugin instead, and perhaps I will in the end.