Need a wiring diagram for 4 way switch with source in centre and light on end
Making the connection in the attic saves you

Here's what you can do with existing cables in wall. 



The black-red grouped pairs are messengers.  On 3-way switches, "C" marks the common. 

Smart switches

That's the sure way to do this thing, but it's a little complicated.  In this case you re-task red as a signal line (as needed by the smart switches).