I'm not sure actually, I would have thought it would be a a Z1-6 cap of £16.30 plus zone 6 to Gatwick £6.60, if you touch in at London Bridge between 1605 and 1857 and it's a weekday - otherwise £4.10.

But Gatwick fares from beyond East Croydon are set at a premium and TfL refuses to publish the extension fares, so it could be more.

If you have minimal luggage you could exit at East Croydon on the way to Gatwick, then turn around and re-enter the station. London Bridge to East Croydon would be included in the Z1-6 cap and ECR-GTW is definitely £6.60/£4.10. You can use your card to pay for this, no need to buy a separate ticket.

I suppose if you bought a paper ticket for ECR-GTW you could stay on the train and get TfL to amend the contactless journey later (otherwise you'd be charged a maximum fare for the no touch out in addition to the actual charges). If you use an e-ticket and it gets checked, they will look for a scan at the East Croydon barriers.