Yeah, it's confusing. I should probably write a new paper just on this topic because there isn't really a good explanation anywhere.
> translate the experiment with polarizer to the experiment with the double slit
Best is not to get too hung up on the physical details. What matters is that a stream of particles can get separated along two separate paths and brought back together, and this can produce an interference pattern. The particular degree of freedom along with the separation takes place (position, polarization, spin, whatever), or the details of how they are split and brought back together (two-slit, half-silvered mirrors, Stern-Gehrlach apparatus, whatever) is mostly irrelevant. What matters is:
1. When unentangled particles are sent through one of these split-combine setups they produce an interference pattern.
2. When you "measure" the degree of freedom along which the particles are split in one of these split-combine setups, the interference pattern disappears and is replaced by a non-interference pattern. (This is just basic quantum mechanics 101.)
3. When you send entangled particles through a split-combine setup what you get is a non-interference pattern, exactly the same as the one you get when you "measure" an unentangled particle. But...
4. If you go through a rather elaborate process (see below) you can separate the entangled particles into two groups, each of which exhibits an interference pattern, and these two interference patterns will add up to make a non-interference pattern. (Even more interesting, there is more than one way that you can do this separation, each of which will produce a different pair of interference patterns, but any given pair will add up to the same non-interference pattern.)
The "elaborate process" involves making measurements on the complimentary observable for one member of each entangled pair, and classifying the other member of the pair into one of two groups based on the outcome of that measurement. This is where the physical details get really complicated for anything other than polarization, where the complimentary observable is just polarization along an axis rotated by 45 degrees to the original.
Note also that the reason that #3 above is true is that measurement and entanglement are actually the same physical phenomenon. The mathematical description of an entangled particle and a "measured" particle is exactly the same.