I am not sure I follow your logic.
There are sensors telling the logic that the main gear is on the ground so it is OK to deploy thrust reversers. Right? So the alert logic should now have an input saying it is OK so don't raise any alerts.
Your 3rd paragraph refers to "delaying unwanted alerts until the nose gear is on the ground". If the nose gear is on the ground, you don't want any alerts, let alone "unwanted" ones.
Bottom line surely is to take the nose gear out of the process?