Firstly, as an aside, note that there is nothing special about bringing the electron to 'rest', as there is no such thing as absolute rest or motion. What you want to do is get the electron in a state of any precise velocity (and hence momentum).
Now the way the accepted (thoroughly tested) quantum mechanical framework works is that if you tell me the state wave-function of a particle in momentum-space (e.g. a momentum eigenstate in your case), the particle's state wave-function in position-space is automatically determined mathematically (by a Fourier Transform, to be precise). And it just so happens that a narrowly defined function in momentum-space corresponds to a spread out function in position-space.
If you want to construct a thought experiment to violate this principle (and that is a very good learning exercise, by the way) you need to give a reasonably clear description of an apparatus which would pin down an electron's momentum (e.g. by a filtering potential) whilst at the same time physically stopping the particle's wave-function from spreading out (e.g. by an essentially infinite potential barrier).
Many people have tried to come up with such schemes, but they all fail.
That's not to say you shouldn't try, because seeing what goes wrong with such proposals provides more insight into what the uncertainty principle really means.
However, just proposing to 'stop' an electron in its tracks provides no reason to doubt that its spatial wave-function will spread out in the process. You need to tell us how you will stop this spreading out from happening, since there is plenty of evidence that it really does happen.
