It's a pity it is early March rather than early April since South Terminal returns on 27 Match. LGW used to offer Twlight check-in but unfortunately it is currently suspended, I hope they restore it from 27 March too.

If it's a 9am start, then you definitely want to take the train, which is reasonably easy even for those taking the kitchen sink. But the best thing to do for that sort of departure time is to stay over in the Hilton, Hampton, Courtyard, Premier Inn or Sofitel (reopens 1 March) since you thereby turn an early morning frazzle into a fairly leisurely check-in process. Room rates should be reasonable.