Okay, so I'm settled on the idea of memory wipes for the droids. But that leaves us with the thorny issue of Obi-Wan's response to them. Does he really not recognise them? Is he being evasive? He doesn't say that he doesn't recognise them, he says that he can't remember ever owning a droid. If he knows that they won't recognise him because they had their minds wiped when they joined the crew of the Tantive IV, then he won't be worried about them giving the game away. But what reason would he have to avoid saying that he knew the droids?
It could just be that he doesn't recognise them. The type of droids which Threepio & Artoo belong to are commonplace machines. But they do have particular personalities. Wouldn't that jog his memory?
If I take the decision to keep the droids as the thread which takes us through the saga, then Obi-Wan will inevitably know them before ANH. This leaves me with having to sort out why he doesn't come out with "Artoo! Threepio! My old friends! How long has it been?"
It's entirely possible to avoid Owen and Beru meeting the droids before ANH. There's no reason why the droids have to be there at any point when Anakin or Obi-Wan are on Tatooine with Anakin's family.
Hmmm...