For the price of a first class train ticket you can probably get a local taxi to take you to Heathrow directly.

I would go with the people voting to get the train down in the morning (2nd class off peak) with plenty of time for disruption. Leaving enough time that I can get a car down if I have to. As we have seen recently trains can go badly wrong on occassion with the north\south route effectively closed for a whole day, so you need a plan B.