You asked what I would have done, ie, the past. There are a ton of things I would have done that would have fixed this issue long ago, the Rangers have ignored it at their peril. They are now desperate for a much needed center, now.
At this stage the best option seems to be either getting Eichel on the cheap if possible then flipping Zibanejad for a package to replenish, or targeting a center who has yet to play in the league yet with a package of defense for offense, maybe the Kings.
They dug this hole though so it is gonna be harder to find a solution.
What they are most likely to do though based on this relatively lousy offseason is pay Mika too much money for too long and then struggle when he declines in 2 years despite getting crippling money.