You may well have made your mind up but here's a suggestion from someone who used to live in Amesbury.
You will see very little more being up close and personal to the stones than visiting at any normal time.
Get the coach link from Heathrow to Woking and then South-West trains to Salisbury.
You can do the Cathedral and the Stones in one day - then back to Salisbury to get a train to Bath.
It's a much nicer city with a lot more to see and do and it;s only about 50 minutes away by train.
Whatever you do don't train it at peak times on the Monday - very,very expensive.
By the way,if you do stay in Salisbury take time to have a pint in the Haunch of Venison - it's one of the smallest and the oldest pubs in the world.