The problem with multiple values in an array is that a checkbox field will not exist in the values sent by the form unless it is checked. In your example, if you kept the names the same and only one checkbox was ticked it would come in like this:

Professor => ["Doe, Jane","Smith, Josh"],
IDNum => ["0116411160645","0116411162016"],
Status => "KEEP THIS ITEM",
[download]

You have no way of telling which item this refers to. So you will need to group each item somehow, and I think your idea of incrementing is fine, as long as you do it to all parameters as hippo points out.