do you show to the Stripe billing option to all installations (meaning also the ones that came directly from the App Store listing) or only the ones that came through your website / are existing customers?

All. That's the issue they've got. It looks like we're going to have to hide it for anyone that comes in via the App Store.

Another problem is we've got 4 products and only one is listed on the Shopify app store. If they log in via product A's listing then buy product B, it seems we must use Shopify's billing for that too.