Using Apple Pay would circumvent the CC tracking because it only transmits a one-use number.
I don’t have an Android device to test these instructions on but they seem plausible and corroborated: https://supportcentre.natwestinternational.com/Searchable/91...
When I made a return for an Apple Pay purchase at Target, they saw that the transaction was marked “Tapped” as card type and took my word for which card was correct. Who knows how long that’ll last. Where I really expect to run into problems down the line is when I try to take advantage of the insurance benefits offered by cards and can’t produce an invoice/receipt with the expected card number on it.