i don't know for certain if greg will see a problem, but the cause for concern is that the bobbins are all oriented in a line. the field extends directly out along the axis of the bobbin/coil, and then wraps back around the bobbin.
stacked on top of each other, as roger suggests, the lines of the field would not align as strongly, though some coupling is possible.
at normal line levels i do not think there will be a problem. the strength of the field falls off sharply with distance, so even a CM or so may be enough distance to avoid problems.
ed