There are 28 players on the current roster that have cap hits of $790,000 or less in 2017. I don't see why that would be different next year.
I just remember back to the Peyton Manning signing and remember the screaming about how they could never sign any other free agent ever again and they'd be over the cap and could never have any wiggle room. Then Elway signed four massive free agents the next season.
I have faith the math would work.