A legendary artefact as compensation is necessary!!
Absolutely, and this is letting Fizzer off lightly. The emotional damage really justifies at least 10 Insane artifacts. Just reading your ordeal, I have sustained damage myself requiring 3 Insanes as compensation.
Regarding Syncing - if he's using the same device & same browser without clearing cache, don't think syncing is necessary as there's nothing to overwrite or conflict with it, but syncing wouldn't hurt. I've seen this issue myself in the past (start dig, come back many hours later, no dig is in progress - but no idea if the dig was still in the undug list or not, didn't track it to that detail).
That said, I don't think it's useful to post bugs with vague details like "I started a dig, then I went back later and it disappeared" b/c that doesn't really give Fizz much to work with to find the cause. Need more specifics, and 1-off's probably don't warrant action/compensation unless the impact is large.