Hi Dave, the orientation in your photo is correct (and that’s the correct way demonstrated in the thread you linked), so I’m a little bit confused about how yours could be fried. It’s possible that the battery isn’t contacting properly. My experience has been that they are wicked hard to push in (because the early versions weren’t tight enough), so I haven’t had any trouble with the coin battery contacting properly.
But in answer to your question, I haven’t repaired the ones in my classroom, but the RTC chip is probably the most feasible chip to repair on the Mayfly. It’s cost is about $7. One of my engineer friends recommended hot air soldering for the removal stage.