Bears haven't had this problem in recent memory where they have quite a few veteran (some near or actual pro-bowl) quality players. You have to have a good number of players on their first contracts to balance it all out. Every year every player, especially those with big contracts, are evaluated. In fact, it's not an annual thing more like a weekly thing.
I did not know that each team is allocated the same amount for UDFAs, unless you are talking about signing bonuses. But eventually once a team signs an UDFA his salary probably would not count against the cap as only the top 50 (or some number less than 53) count against the cap and if they do they'll be at the bottom.
As for the cap cuts you identified for next year, I'd agree with Prince, maybe Long, Gabriel is iffy and Burton unlikely. It all depends on the productivity of the player and the potential productivity of the player that replaces him.