Past = Memory,
Future = Prediction,
---> allow us to have a sense of continuity
---> self-awareness
---> sense of self and attachment?
What if we break all of these things apart and treat them as they are individually?
Will we understand the mind better this way?
Is this the key to enlightenment? Is this what they mean by dissecting the mind?

You must compartmentalize the 5 khandas as pointed out by Acariya Maha Boowa in The Path to Arahantship.

Yes, break them apart and analyze them individually.