The work around is to wait, my pure speculation,
Girardi will be bought out before the expansion draft (and it's not really pretty). Or perhaps he ends up on permanent LTIR if his injuries are degenerative. He makes more money by not being bought out at 2/3rd his remaining as it's unlikely he gets another contract after other than something like Carle(700K) and even that may be a stretch.
Staal I think he is on their LD for the foreseeable future, like for years, His contract even without the NMC is tough to move. The actual salary does not go down by much and he has a 3M signing bonus in the last year of it. It's not buyout friendly or attractive to lower spending teams. If he plays somewhat well this season perhaps some team show a bit of interest but not without a sweetener added, and even then the sweetener would be something the Rangers are better off not giving up just to get out of the Staal contract. Or maybe they can find a acceptable cap dump equivalent to Staal (no not Moulson) but someone serviceable that is just also carrying a much higher cap hit than he should, yet still NMC.
Rangers are stuck for a while with those two cap hits (or similar) one way or the other. It's why trying to add in larger contracts to this team does not make sense, they are not going to improve much by doing so and they have other players to extend, so they stayed out of UFA for the most part, signed short deals, and why they SHOULD not be moving assets for contracts like the next Shattenkirk deal.
Ranger fans, we have to hope that Sather is out, like for reals, everything he did since their Cinderella cup run has been poorly thought out. Stralman, Hagelin, Duclair, the 1sts, 2nds,... Rangers need to basically do the opposite, sell for 3 or so years just to maybe get back towards trending up. They are not winning anything with like ~12M (~13M if we include Glass) in basic cap dumps within their cap structure.