How about (and I have done it when I learnt that M25 is stuck
Heathrow Express (15 minutes) + Taxi Paddington - Victoria about 20minutes. You can tube it, but with luggage a pain and then Gatwick Express 30 minutes. Even with bad connections you still be able to do it comfortably in 90 minutes. The cheapest minicab I have found was Purple Airport Cars (£60).