Most definitely CJ will have to come off his demands a bit. He'll be 30 on any new contract. I think the hangup, much like on Tyreek before we traded him, is not AAV, but guaranteed %. Also his agents being newbie idiots is a barrier.
That said if there's some middle ground to be had, signing CJ does not preclude us from re-signing anyone we want as I have said before. Following Veach's preferred contract model the first year cap hit is usually quite low.
Assuming the projected cap increases are correct (they may actually be higher depending on revenue) we have 30m+ in cap space next year and 124m+ the year after, including Mahomes new contract. After that the cap number is almost irrelevant as it will be a mostly new team and who knows what that will look like, but fwiw the following year we have 299m+ in cap space.