Anonymous #20 said: You know, I should have just checked the dictionary. It turns out that 'though' can be used as an adverb and in that usage my sentence is correct. 
You're right, though: that semi-colon could easily have been replaced with a comma.
Hooray! Balance has returned to the grammatical force.
Sorry, that would only apply if the word "though" was being used as a postpositive modifier of the phrase "you're right." In your sentence, "though" is a parenthetical statement, as it can be removed without changing the meaning.
"You're right, that semi-colon could easily have been replaced with a comma."
OR
"You're right: that semi-colon could easily have been replaced with a comma."
OR
"You're right, though, that semi-colon could easily have been replaced with a comma."
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