If staying overnight near Paddington, the morning Heathrow Express can be the most reliable choice

https://www.scribd.com/document/1074920514/Getting-to-Heathrow-from-Gatwick-Easiest-Inter-Airport-Transfers-178501

If staying overnight near Paddington, the morning Heathrow Express can be the most reliable choice, beating rush-hour road traffic across west London.