> At the moment, most of our transactions are done the latter way (get billed by airline/hotel/etc and then separately charge the customer)

One concern that comes to mind about this is if the credit card companies would consider this purchase as "travel". Like where Chase Sapphire Reserve gives triple points for travel purchases, and also has a $300 travel credit, but either of those things would only work if Chase considers your service as "travel", rather than "online service" or whatever.

You may have already worked this out and gotten it classified as travel, and if so it would just be a nice thing to put on a FAQ or whatever.