Basically, in using this process, i used a numerical value for the second part of the substring which was longer than the len of any of the rows in that table. So my queries wound up looking like:
Update GCSOSUBJECTS set COUNTY=SUBSTRING(COURTNAME,8,20) where COURTNAME LIKE 'COUNTY-%'
Update GCSOSUBJECTS set COUNTY=SUBSTRING(COURTNAME,9,20) where COURNTNAME LIKE 'CIRCUIT-%'