How do I calculate the total cruise power from the propellers accounting for the losses?
The flow leaving the propeller:


Contracts, as a function of distance behind the propeller. The impulse theory gives a contraction factor - for an idealised homogeneous outflow field. The contracted wake has a higher velocity than free stream.
Has a whirl component due to the drag of the blades.
Has propeller tip vortices in a contracting corkscrew field.


So if the aft propellers are far enough behind the forward ones, the aft propeller tips are unaffected by the wake of the forward ones. 

If the aft prop counter-rotates, the whirl component from the front props will be removed. Optimal blade angle of the aft prop is different from that of the fwd prop, but the tips would remain relatively unaffected.



Picture above is from Leishman, which has a whole chapter devoted to rotor wake. There has been quite some research done on co-axial rotors for helicopters. There is some info and a link in this answer as well.

But I reckon you'll be in the right order of magnitude if you just compute required power as you would in an undisturbed flow, especially if you use ducted propellers which reduce the tip vortices.