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I've found out Stripe wasn't even necessary to begin with. There are plenty of payment gateways (double-digit number of them) in the jurisdiction where the foreign parent entity would be located. Moreover, Stripe is actually offered in a lot of countries besides the U.S.! The post https://hackernoon.com/stripe-atlas-is-not-for-everyone-cave... made some really good points, including this:

> Unless you have a really crappy situation with respect to payment processing, regulations etc., that are real roadblocks for competing internationally, I do not recommend setting up company for the romanticised notion of using a particular gateway.

I made that mistake of romanticizing Stripe. I was too hasty, and didn't bother to do some basic research. Customers just want an easy way to pay, and definitely don't care what gateway you choose to use. As far as setting up an American company/subsidiary goes, it's not worth the trouble. Reading https://stripe.com/atlas/guides/business-taxes alone was eye-watering and migraine-inducing. The plethora of complicated tax rules are absolutely not worth enduring just to use one particular payment processing system.