I’m trying to book INV to LHR and then LGW to MCO the next day (less than 24 hours between flights) to avoid changing airports on the same day.

The normal booking engine only gives me the option of AA from LHR the same day, connecting in Miami.
When I use the multi-city option I can book the flights I want but it is £110 more expensive than LGW to MCO. I had assumed (perhaps erroneously) that it would be cheaper from INV due to avoiding APD.

Does anyone know whether it is possible to book these flights with a lower price?

Thanks.