High speed 24 hour train direct link between Gatwick and Heathrow is the future proof solution. It's 25 miles as the crow flies, so at an average speed of only 50 mph, thats a 30 minute journey on a train. At an average speed of 100 mph, that's a 15 minute journey.
Instead of looking at the Gatwick options as a negative, look at it as a positive.
Three Runways at Heathrow
Benefits: Three Runways at Heathrow, increasing capacity as a transport hub by presumably 50%
Drawbacks: 1) The runway would cross the fecking M25, so that's a massive cost. 2) Probably increase the chance of a major accident due to high traffic in the skies, and closeness to M25, M4 and London in general.
Heathrow- Expanded Gatwick Train Connection
Benefits: Two runways at Heathrow and two runways at Gatwick increase capacit as a transport hub by presumably 100%
Drawbacks: You need to build another expensive underground train line. And then give away tickets on those trains for free.