I'm assuming one of your Railcards is loaded onto your Oyster card.
The absolute cheapest way to make the journey would likely be to use Oyster from Clapham Junction to West Drayton avoiding Zone 1 (£1.70 each way), and then touching out to continue your journey with a paper ticket or eTicket to Iver (£2.90 return). It would be a rather slow and convoluted itinerary, but it means a total cost of only £6.30.
Touching out and back in at Hayes & Harlington is slightly more expensive (£1.65 Oyster each way + £3.45 return ticket = £6.75) but reduces the journey time since the frequency there is much higher (10tph under the standard timetable) than to West Drayton (4tph). The likelihood is that you would simply step back from a Heathrow train onto the same Reading/Maidenhead train you would have ended up catching anyway.
Alternatively if you want to be 100% sure you can jump on the first train, you could use Oyster from Clapham Junction to Ealing Broadway (£1.50 e/w avoiding Zone 1), then touch out using the yellow platform readers and continue with a paper/eTicket return (£4.90) making for a total cost of £7.90. If you buy an eTicket on your phone, you could decide which of the above two approaches you go for once you're on the Central line and are approaching Ealing Broadway - since you'd know what the next Elizabeth line train is that you can make.
For the quickest interchange, you want to be towards the back of the train at Shepherd's Bush and at the very front of the Central line train at Ealing. Yellow readers are located at the entrance to Clapham Junction platforms 1 (for the Mildmay line) and the Central line platforms at Ealing Broadway. If you use one of the hourly Southern services from Clapham Junction the closest yellow reader to platform 16, which that service uses, is on platform 17.
The quickest journey without any stepping back would require a paper ticket from Underground Zone 1 to Iver (£12.65 return) but I imagine you didn't post here to ask about that
