Do superconductors actually have really, trully, honest-to-Omega zero resistance, or is it just low enough that we can ignore it over really long time frames?

It's for-real zero. (Source: conference La supraconductivité dans tous ses états, Palaiseau, 2011) Take a superconductive loop with a current in it and measure its resistance with a precise ohmeter. You'll find zero, which tells you that the resistance must be less than the absolute error on the ohmeter. This tells you that an electron encounters a resistive obstacle at most every few ten kilometers or so. But the loop is much smaller than that, so there can't be any obstacles in it.