Atkinson's situation is mostly irrelevant next season, I think. There's a certain sunk cap cost for him...which is only a small of the total Flyer's already sunk-cap cost...so whatever happens to him, it can certainly be viewed from the Flyers viewpoint as "whatever the best fit is, without spending any more cap."
So buy-out seems pointless. Forced to play wherever the Flyers deem suitable seems likely. LTIR'd into cap assets seems fairly reasonable, doesn't every player at that age have sufficient injuries to warrant being LTIR'd? They're professional hockey players after all....if Kucherov and Stone(x2) can do it, Atkinson certainly has it in him. Hell, Ellis only needed 5 games to manage a career-ending story, for a team that wanted him to play! Atkinson can manage that for a team that doesn't want him to play..