> Now I have to make the source available, correct?
Nope! That's one way to fix the licensing issue—but you're not forced to do that.
Another option would be to immediately stop distributing your binary and not distribute it again until you can replace or otherwise excise the GPL code that caused the licensing issue.
Eh, that is a bit dishonest argument. "I want to keep distributing, and I want to keep using this code" are the immutable assumptions of my argument. My point is, with those assumptions in place, there is no way to NOT propagate GPL in the entirety of the work - was my point. That is OK since GPL is intentionally made that way. Take it or leave it deal. No one is entitled to anything, if people want to distribute their work as GPL, that is up to them to decide after all. I am only discussing the virality aspect of it here as a separate fact.
And how does immediately stoping distribution help, legally? If I have already distributed the binary, the recipients are already entitled to the entire sources, no? Or does GPL have a "I have learned my lesson" clause?
Nope! That's one way to fix the licensing issue—but you're not forced to do that.
Another option would be to immediately stop distributing your binary and not distribute it again until you can replace or otherwise excise the GPL code that caused the licensing issue.