[pron]

The thing is, what does it mean to "work around"? It is true that the halting theorem in its classical formulation can be "worked around" like this, but the classical halting theorem is not the one that matters in practice. What matters in practice is what's sometimes called the bounded halting theorem (which lies at the core of the time-hierarchy theorem), which roughly states that you cannot tell whether a program will halt on input x within n steps in fewer than n steps (and a corollary is that you cannot in general extrapolate information from one input to another). Bounded halting -- which is proved using the same diagonalization proof as the "classical" halting theorem -- is pretty robust. It holds for total languages and even for finite state machines.

So what really bothers us about the halting theorem is that -- in general -- you cannot tell what a program will do with some input any faster than actually running it, and this, bounded halting, is not something we can work around.