Keep in mind everyone else will have the extra cap space too, which may actually mean Callahan and other second-tier free agents (like Amos) wind up costing an even larger percentage of the cap as more GM's find themselves with resource flexibility to shore up a weakness like nickel back.
What I would look into if I were the Bears is using this money to see what happens with the franchise tag. Landon Collins has publicly said he'll make a big fuss if the Giants tag him, and after the Bell situation where Pittsburgh totally screwed themselves I wonder if teams will be reticent to still ignore that kind of bluster from players anymore. Adding Collins or Mathieu would be a massive upgrade over Amos, more than offsetting the loss of RRH and Callahan.
The other option, which can be done on top of upgrading safety, is finding a way to find a complement to Mack the way the Clowney is to Watt or Ware was to Von Miller. Much less options there since I am terrified of Dee Ford and know there's just no way Frank Clark or Jadeveon Clowney are hitting the open market...but Bears can still get crafty.
Luck is going to bounce the other way for the Bears a little next season and they'll have a tougher schedule. Assuming the Bears win the division they are going to play the Rams and the Saints (as opposed to this year the Giants and 49ers). They will need to stay ahead of that by adding some truly elite talent. Keeping standouts like Callahan and RRH would be great, but they are both a cut or two below elite-level (Callahan more for durability issues than anything). Let them walk and enjoy the 3rd or 4th round comp pick in 2020, by then they'll be really needing the draft capital. In the meantime refocus the assets on another elite talent that can keep, or even elevate, the defense's level during this window the Bears have.