Should the questioner continue managing a forum after having modified its content to conform with Islamic law, given her fear of being held accountable for what might be written in it in the future, and knowing that if she leaves it, it will revert to its previous state of violations?

If leaving the forum means that the questioner will revert to their previous state before becoming committed, then they should not leave the forum, even if it contains some violations. This falls under the principle of averting the greater of two evils and achieving the greater of two benefits. The questioner must fear Allah and change what is wrong to the best of their ability.