It is likely a reciprocity failure issue. It is also likely that the standard variations are also at play. Meters, shutters, processing details, etc. However, since the problem is only popping up when you are using tiny apertures and hence long exposures, I think reciprocity failure is the main culprit.
You are not shooting blind at all. You have a meter, which is more than most people had when they made some of the greatest photographs ever. Polaroid is good for previewing the composition and lighting, but fairly useless as a check of exposure; especially when you get into long exposures. I have only ever used Polaroid when I want a Polaroid, not as a substitute for a meter. It is a shame to see it gone, but you don't need it by any stretch.