Thank you for the balanced take on an extremely spicy topic.
At WePay (YC S09) we debated this extensively and came up with a similar middle of the way solution. Making sure that a credit card can get tokenized is the critical flow and should run every minute. We ended up with about 4-5 very quick production tests. They helped with debugging as well as alerting.
I am now building a full, automated testing solution at Donobu (https://www.donobu.com), and production tests definitely come up as their own subcategory of e2e tests. I am going to use your guidelines to refine our prompt and bound our production test generator.