There is talk that Boris Johnson wants to get Biden to open a travel corridor between the US and UK and he is rumored to be addressing this issue with Biden at the G7 summit next week. I would hold off changing your SFO-LHR flight since I doubt you will be able to keep your discounted Avios pricing if you change it. If the travel corridor happens it may happen by the end of June.

To protect the trip I would book a backup connecting flight LHR-ATH using Avios (so you could cancel it if it is not needed). My understanding is that you can use the UK PLF to specify that you are transiting (even on separate tickets so long as less than 24 hours?) and mark that you are exempt from the day 2,8 Covid testing booking requirement on arrival to the UK (because you are really only transiting), but you still need the pre-departure Covid test.

Check:

https://www.heathrow.com/customer-su...t-restrictions

and

https://onemileatatime.com/uk-passenger-locator-form/
[Ben at OMMAT shows how to fill out PLF form]

Edit:
Updated the Covid testing info.