Review the original item:
Professor Britton was grading papers at her desk,
her students were slaving over their in-class compositions, sighing
heavily and flipping through their dictionaries for the correct spellings
of words.
You wanted to fix it this way:
Professor Britton was grading papers at her desk,
moreover, her
students were slaving over their in-class compositions, sighing heavily
and flipping through their dictionaries for the correct spellings of words.
A comma splice—a major sentence error—occurs when you have two main clauses connected with just a comma. Professor Britton was grading papers at her desk is one main clause. Her students were slaving over their in-class compositions is a second main clause.
The conjunctive adverb moreover doesn't change the fact that you still have two main clauses connected with a comma alone.
You might want to consult the rules for fixing comma splices and fused sentences.