I think you're being incredibly optimistic. And maybe a bit naive if you don't think Laf's and Fox's agents aren't going to want huge deals for their guys. Especially after seeing the Rangers bringing in a guy making 10m. And again, you'll have one good center on the team after next season and much less ammo (players, picks, and cap space) to go out and get the other two.
Well, here are the numbers. With Eichel on the roster, you have $59m committed and $22m available to spend with no real pressing needs due to the youth that keeps coming up. Presume for a minute that the roster remains untouched - you have that much money to re-sign Buchnevich, Chytil, Gauthier, Howden, DiGiuseppe, Brendan Smith, Jack Johnson, Ryan Lindgren, Libor Hajek, and Igor Shesterkin. This cap space is counting DeAngelo - if his contract is terminated, that cap space becomes $26m+ instead.
I would also presume at least one of those names is out the door in the trade - either Buch or Chytil or both. For simplicity, let's assume Buch and Chytil both go in the trade, Strome stays to play 3C, and Kravtsov is called up to fill the RW roster spot (whether or not he can do this as well as Buch does is obviously up for debate and discovery).
So $26m. I'll keep running totals in parentheses.
Gauthier, Howden, DiGiuseppe, and Hajek get not much more than the minimum (~$4m). So does Kravtsov on an ELC (now at ~$5m). Smith and Jack Johnson both depart (hopefully). This leaves you at $22m or so with the need to re-sign Lindgren and Shesterkin to sizeable deals, plus fill in the margins with cheap replacements for Smith, Johnson, etc. I think you can actually use the flat cap in this situation to skip bridge deals for Lindgren and Shesterkin and sign them to very reasonable long term deals. Maybe $4m for Lindgren and $5m for Shesterkin. (We are now at about $12m in space).
Roster (lines are just throw together to get names down, not actually proposed as ideal lines):
Panarin - Zibanejad - Kakko
Lafreniere - Eichel - Kravtsov
Kreider - Strome - Gauthier
Lemieux - Howden - Blackwell
X: Rooney, PDG
Lindgren - Fox
Miller - Trouba
Hajek - _____ (? Reunanen? Bring up Robertson? Schneider? I'm presuming Lundkvist dealt for Eichel or that is his spot).
x: cheap 7th D
So this all works for 21-22 with ample space remaining (~$10m or so).
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Moving on to 22-23:
Zibanejad, Strome, Lemieux, Kakko, Rooney, Blackwell, Fox and Georgiev have contracts expire. This frees up about $16m in space, plus the $10m we carried over from last season, for a total of about $26m.
Georgiev can be traded or allowed to walk. A cheap backup option is in the cards as Shesterkin has embedded himself as the starter on a long term deal most likely (~$25m left). Strome is probably also either traded or allowed to depart and another mid-tier 3C acquired somehow (let's say he commands a similar ~$5m salary). (~$20m left).
The big names to re-sign here will be Zibanejad, Fox, and Kakko, and there is $20m to play with. Zibanehad is probably not going to top $10m given this season unless he truly explodes next season. Kakko similarly given slow production his first two years is not going to command a megadeal.
Fox probably will get a sizeable deal. If you can get him on a solid long term contract, great, because that deal will soon start to look amazing as the cap explodes the following year. But I think it's entirely reasonable to suspect Zibanejad may be more along the lines of $7m-$8m, Kakko more like $4m. Can you get Fox locked up long term for $8m? Probably, if not less. If no, then you can bridge him and put off that fight to another day.
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Too many variable to keep this exercise going, but the point is, things are not desperate. The following season, the cap begins to rise, with only Miller and Lafreniere as your big ticket re-signings.
I'm just not that worried. It's all doable.