Thanks so much for your help with this, the results look much more like they ought to. A few census blocks remain outliers but I believe this is due to some kind of bad connectivity in the network. I've attached some images just in case because I am still learning to use network analyst.
It appears that for the outlying census blocks, if I run Service Area analysis, the results are in line with Calculate Accessibility Matrix, and you can see that the connectivity is limited when lines are displayed. If I change the streets layer in the Network Dataset to "any vertex" more of the census blocks have expected outputs (but not all, these have been selected in blue).
If there is any suggestion you might have on how to adjust, repair or account for these weird phenomena in the network it would be greatly appreciated. I will mark your last post as the solution though --- as I believe for anyone else experiencing an issue like mine, your bug fix will likely fix their issue. Again, thank you so much!