Is there a code-compliant way to label a wire where the conductors are not wired in the expected way?
Nope, you can't loop power out one cable and back the other.

The rule is that currents must sum up to zero (be equal and opposite) amongst all wires in each cable or conduit. 

That means your idea of 3 cables - one for hot+neutral and two more for four switched lines - is a non-starter.  You would need ONE cable that is /6.  Or alternately, conduit and individual THHN wires.  (No, you can not strip NM's sheath and use the individual wires, unless they are marked, and they're  not.) 

As such, the three cables are useles, and this has an effect on the landscape.

You can't eliminate the stairwell switch

Code absolutely requires stairwell switches at top and bottom.  So that one needs to stay. The alternatives are motion sensors that are positioned correctly (hard), or lights left on 24x7. 

Go back to your original plan

You have four cables or things that are only always-hot: supply, doorbell, smoke, and onward power to this lamp group.   That is 8 conductors, 1 for all grounds, 1 for all cable clamps, so 10 "wire count".  With 12 AWG wire that is 2.25 cubic inches per "wire", giving 22.5 cubic inches total.  A tick too much for a 4x4x1.5" steel box, so go with a 4-11/16" square steel box (42 c.i.), or a 4" deep (30.3 c.i.).  

What does that leave in the switch box? Power supply, one /3 cable to the 3way, four /2 cables to lamps, and three yokes.   That's 11 conductors, 1 ground, 1 clamps, and 3 yokes.  A yoke counts as 2 of the largest wire attached to it, so 6+11+1+1 = 19 "wires".   At 2.25 cubic inches per, that is 42.75 cubic inches needed. 

Look at your plastic junction box, they are pretty big so good shot.  

Conduit

If that doesn't work, you'll need to change to the conduit wiring system so you can splice all those neutrals in a seeparate third box. But the problem is those plastic boxes don't have entry points for conduit.  

Your better bet would be to change the plastic box for a metal one, and let the switches ground through their yokes.  All grounds are free, but that doesn't mean they don't take practical space.  If your metal switch box then fed to a metal junction box nearby with metal conduit between, all that conduit becomes the ground, and the NM cables only nee to tie to ground wherever they enter the metal piping system.