I think you guys are forgetting - the provisions in the FEA here are reinforced in Article I, Section 4 of the Constitution itself. The correct way to do this would be via constitutional amendment first - *then* by changing the statute.
For amending the constitution, and fixing the other issues people have brought up, I'd again strongly suggest the Senate take up the proposal introduced by Wulfric in the House:
The No Moderator or Accidental Invalidation Amendment
Article I, Section IV of the 4th constitution shall be amended to read as follows:
The right of citizens of the Republic of Atlasia to vote shall not be denied, except in regards to persons whose account is fewer than 168 hours old, as punishment for crimes of which the accused has been duly convicted, or in consequence of failing to meet such requirements for frequent posting or term of residency as may be established by law; but no ballot shall be counted as valid that should list the candidates for office in a script other than the Latin alphabet, or that has been edited more than twenty minutes after its posting in the voting booth. All posts made in the voting booth shall be considered as ballots, and no citizen shall cast multiple ballots in any one election during the period the voting booth is open, upon penalty of the invalidation of their vote, unless:
1. Evidence exists that the first ballot submitted by the citizen was deleted by a Moderator or Administrator of the Atlas Forum, or
2. The second ballot submitted was clearly accidental as it only lists contests not up for election within the thread it was posted on, in which case only the first ballot shall be counted, or:
3. The second ballot submitted was clearly accidental as it is identical to the first ballot and was submitted within five minutes of the first ballot, in which case only the first ballot shall be counted.
However, in no circumstances shall a user be allowed to cast a third or subsequent ballot in any election, upon penalty of invalidation of all ballots submitted.
(Keeping the moderator part is up to you, but I think the duplicate ballot clauses here work better.)