Unfortunately, it will be a bit of a hit-or-miss situation. You are depending on expired chemicals spreading evenly, and from my experience there is not a whole lot one can do about it. Creating a project from a limited supply of expired Polaroid material is a chancy thing -- as you are discovering. If the chemicals do not spread evenly, then there is no development in the areas that do not get the chemical -- thus the black.
I have had similar results from expired Type 55. Only thing I can think of is that if you get a good image in one or two tries, save the third one for the next portrait. That and embrace the "mistakes" and include them in your project if there is any image at all.
I have some Type 69 that is bad because it was kept flat for too many years and the pressure of the pods on the film above and below it has caused discolored prints -- found out way too late that the boxes need to be kept up-right on its short end...fortunately this problem does not seem to extend to the Type 55 (so far).
Check your rollers to make sure they stay clean. I have not heard of anyone "massaging" the chemical pods -- but who knows, perhaps that would help, though there are chances of popping the pod, which would nasty.