The resolution that works for me is:
- We claim it's guaranteed that a fire alarm happens.
- We claim it's guaranteed it will be a surprise.
- Through logical deduction we can argue that if the 2nd statement is true, the 1st statement cannot always be true.
- So therefore, the original two claims were already inconsistent - they can't both be true at once.
The problem comes when you assume that because the original system was inconsistent, the 1st statement must be false. At the point you prove inconsistency, all bets are off, because you can prove anything you want from a contradiction. You can prove a fire alarm can't happen, and you can also prove a fire alarm can happen.
Suppose we instead concluded that each statement may or may not be true. Then, even on the last day of the week, we don't know if a fire alarm will happen or not. So if it does, it'll be a surprise. And if it doesn't, then well, I guess the 2nd statement resolved to false.