I'd sign both if we had a new owner and could spend to the ceiling.
In our current situation, I think we need to look at what we can do to best set the team up five years from now when they move to a downtown arena and the possibility of a change in ownership or at the very least outside investors is increased.
Attendance is already bad, the brand is severely damaged locally by being intertwined with Melnyk's toxic brand. Even if we retain both Duchene and Stone, because of our inability to spend, we'll never be able to build on having the two of them in their prime, and we'll at best be a playoff bubble team in our better years where everything clicks, and this is a huge long shot.
We are entering a period where all the arguments against deliberately losing are irrelevant because all the negatives that come with tanking (poor attendance and fan interest, players not re-signing, not making the playoffs) are already happening regardless of whether we choose to tank. With that in mind, we might as well tank in order to enjoy the long term benefits that come with that strategy.
The most productive thing we can do right now is to build up assets and a pool of top prospects in order to put us in a position where if there is a change of ownership a few years down the line, we can actually build a team and keep our players. Signing both Duchene and Stone is counter productive to that.
I would keep Stone because he is younger meaning he is more likely to still be a top line forward 4-5 years from now, and his leadership would be extremely valuable through a tough few seasons of losing. While Stone is one of the best wingers in the league, if we are losing a majority of our veterans, including our only solid goaltender in Craig Anderson, I find it hard to believe that Stone alone will be enough to push us out of the basement and sabotage our ability to finish as close to last place as possible and rack up 4th OA or better picks.
Matt Duchene will be 29 years old next season. If we keep both Duchene and Stone the consequences would be;
-Makes our team better, we don't get as valuable draft picks, but we aren't likely to be good enough to make the playoffs.
-Nearly 30 million tied up in Duchene, Stone, and Ryan increases the odds that we have to bridge players like Chabot, Tkachuk, and White. Bridging those players increases the odds of them walking as UFAs or having to be traded earlier on in their careers compared to if we cost control them as early as possible.
-The cap is going up, and there is a possible new US TV deal on the horizon. Being forced to bridge key young stars at the expense of a player who'll be in his mid 30's by the time this "rebuild" gains any momentum could destroy any prospect of contending or even just being a playoff team before it happens via making some of our best players too expensive to keep beyond the age of 27 or 7 year mark because they weren't cost controlled coming off of their ELCs, and a rising cap along with arbitration and/or their UFA status increases their ability to bargain for much larger salaries than they'd otherwise be signed to right off their ELCs.
Therefore, I would attempt to sign Mark Stone, and I would trade Matt Duchene. The original Matt Duchene trade has set this franchise back years, and the only way to equalize against that would be a trade where Duchene signs an extension and as a result we get a young blue chip prospect back among other pieces. Even if that's not a possibility, and we have to trade Duchene for a soft return, it's not worth keeping him just to save face if it is not the right strategic move. There are indirect benefits to trading Duchene, namely freeing up salary space to help sign Chabot and/or Tkachuk to long term deals right off of their ELCs (this is a very finite resource), and making our team significantly worse going into 2020 in order to help ensure we get the best shot at whoever the top prospect is in that draft (currently Lafreniere).