My wife works near East Croydon station and does this run once a month or so. Train to Victoria (takes about 15 minutes, very frequent trains). Then get to Paddington (might as well take a taxi at that time in the morning, won't cost so much). Then Heathrow Express to Heathrow (takes 20 minutes, every 15 minutes). Allow about an hour and a half in total.

I would suggest to avoid buses etc because of traffic uncertainty, and avoid the tube as the link to T4 hasn't yet reopened. Also, because both trains above run so regularly, you won't have to stand around waiting for anything for very long.