Starring at this data more: I see a few common substitutions:
'0' for '°', which is 48 0b110000
'1' for '±', which is 49 0b110001
',' for '¬', which is 44 0b101100
'.' for '®', which is 46 0b101110
'7' for '·', which is 55 0b110111
'2' for '²', which is 50 0b110010
What's even more confusing is that many of these chksum correctly. So... I'm left wondering if something is going wrong that's unrelated to the actual device, but rather my handling of character data. I would guess that I was messing up the sign, but the characters above that are wrong don't appear to be wrong by their initial binary digit.