I am not sure I understand your thought that Dallas doesn't have the money. Most years they base restructure the three linemen Smith, Martin, Collins -- if all they do is that, according to Sprotrac they have 8M to spend. Base restructure Dak and Coop and they have 33M. That is without restructuring Tank or Elliot.
I think Dallas is all in with these 5 players throughout their contracts which go no longer than 2025, and still allows them to sign whomever they want. Even if they give Gregory 15M, they still have enough to pay quite a few others. If they want to add a big name, they just have to restructure Tank and gain 9M or Lewis for a M if they only need a small amount.
I think if Dallas gets close but doesn't win it all this year, Dallas will be all-in next year and probably sign a big name like Wagner or Von Miller or someone else they think will put them over the top.