You have the solution in your code:

#WRITE NUMBER BACK
open(FH, "+< counter.dat");
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This opens the file for reading and writing, so this should work:

#READ NUMBER, INCREASE AND WRITE NUMBER BACK
open(FH, "+< counter.dat");
 flock(FH, 2);
 $id = <FH>;
 $id++;
 seek(FH, 0, 0); truncate(FH, 0);
 print FH $id;
close(FH);
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