No chance of adjusting your schedule to permit transfers between LHR and LGW? Other than taking a couple of hours I don't suppose it's too painful. I've never done it myself but remember seeing a Gatwick Transfers sign at LHR the other day, so I expect there's a direct coach service.

I think folks have asked here about the consequences of skipping a couple of segments. You might take a look at those threads and decide if that's a $75+ activity, or likely to go unnoticed.