... no matter how I reference that [hash] variable ..., [it] always begins at "1".

From the behavior you describe, I strongly suspect you were not running with strictures and warnings enabled; had they been, you would have received some useful hints. In the first example below, run without strictures and warnings, the scalar variable  $hash is created and initialized, but there is no  %hash hash variable created explicitly; instead, it is autovivified.

>perl -le
"my $pbxex = 42;
 my $hash = $pbxex;
 ;;
 for (qw(CS EE EE CS EE)) {
   $hash{$_}++;
   printf qq{'$_$hash{$_}'  };
   }
"
'CS1'  'EE1'  'EE2'  'CS2'  'EE3'

>perl -wMstrict -le
"my $pbxex = 42;
 my $hash = $pbxex;
 ;;
 for (qw(CS EE EE CS EE)) {
   $hash{$_}++;
   printf qq{'$_$hash{$_}'  };
   }
"
Global symbol "%hash" requires explicit package name at -e line 1.
Global symbol "%hash" requires explicit package name at -e line 1.
Execution of -e aborted due to compilation errors.
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If I correctly understand what you are trying to do, I would think that something like toolic's approach would be best.