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.

Decidability (as a property of decision problems like the halting problem) is a different notion, though: In the context of incompleteness, an undecidable statement is a statement that cannot be proven or disproved in that system. Decidability of a decision problem is concerned with an effective procedure that, for every instance of the problem, answers yes/no. Specifically for a logical theory, decidability of this theory is deciding for any formula in the same language whether it follows from the theory as a logical consequence.

Neither incompleteness nor undecidability imply the other[0].

[0] https://en.wikipedia.org/wiki/Decidability_(logic)#Relations...

Tortoise/hare loop detection also works pretty well for short-cutting Mandelbrot set iteration :-)