Thank you for your replies and I appreciate the workarounds from kwisstan and Knickam. However this seems to give me (publicly-available fares plus cost of rental) minus a small discount = still expensive.

Doing it the standard way seems to draw fares from invisible cheap fare buckets and produce very heavy discounts.
eg LHR - HAJ this weekend
If booked separately £597.40
Total discount - £359.40
Total price £238

In an example such as this if I saw same-day Avios availability on a later flight back, I would be tempted to take a risk and arrive at the airport 45 mins before the originally-intended flight, in the knowledge that if I missed it I could still get home cheaply. But the 2 hour rule on the return of the car effectively prevents me doing this.

I think that asking the counter staff when I take the car to amend the return time, might possibly work as my limited experience is that the Avis counter don't recognise this as a specially-discounted "BA Holidays" booking, and just treat it as any other Avis Preferred booking (providing you enter your Wizard number when booking).