Unfortunately, AFAIK there is no official scipy binary for 64-bit windows, nor an officially supported way to build it yourself (that is why pip fails). The problem is the lack of a free 64 bit Fortran compiler. The Christoph Gohlke builds you linked to use the Intel Fortran compiler, which gives good performance, but has some unfortunate problems. That said, I have used scipy.optimize with those builds, so I don't know it isn't working for you. You may be on the right track with numpy I always install the entire numpy/scipy stack from the same place.
Your options are basically 1) switch to Linux or OSX where 64-bit is fully supported, 2) Switch to 32-bit python where you can use all the official distributions, or 3) install multiple versions of python side-by-side. virtualenv can help with this. Of course, all your numerical code will have to work with the new version, but at least you can keep the system python version intact for whatever else it needs.