What an excellent description of your experience!
Since I did not follow up my earlier message, here it is. After contacting Chipotle by email (in which I reported an indifferent attitude about what it means to not have gluten), they responded to me that they would be contacting those two stores.
But, as you and others have described so well - there are many opportunities for cross contamination even if the server is being as diligent as possible! Depressing, no? As far as that heater/presser goes, before putting a gluten-free corn tortilla on it, it should really be cleaned, or, as in your case, skipped.