Thanks for your feedback! While I haven't yet had any freezes, I have now implemented your timeout idea, just in case.
As for the wireless, I'm using the CYWM6935 board, which (annoyingly) has 2mm pitch headers, and that is why you see it hanging over the part of the board to which it is attached.
I kept the measuring and drawing arrays separate for the sake of accuracy. My reasoning is that if the radio waits to draw the value of the current channel on the lcd (which can be pretty slow to respond), before moving to the next channel, then the times at which each channel's measurement was taken are further spaced apart, and the full portrait of the spectrum is less accurate.
However, I did add a line to the drawing loops to check if the measurement has changed, and I also added that fix in the drawing algorithm (which is a really good idea) and it seems to be running slightly faster, so thanks for that.
Thanks again!