Ok, thanks for the added information.
Let me first explain the original wiring and then you will understand this statement.
The white wires in the Kitchen switch box are NOT neutral, that is the main hot from the light.
This is how it was originally, if you have provided the count of all wires in all of the 4 boxes correctly. Nothing missing.
They ran a 14/2 cable down form the light to the kitchen switch.
In that cable the white is power and the black is the load, the wire the light is connected to in the ceiling box.
That white wire then joined the next white in the 3 wire cable to the 2nd switch
Then form the 2nd switch to the 3rd
And the 3rd to the 4th
The 4th switch was originally one of the 3 way switches, so that white wire was on the black screw on that switch.
So, you had power to the 4th switch and the light on the #1 switch.
That is standard 3 way wiring, as only one gets the power and the other gets the wire to the light, or the load.
The 4 way switches, only switch the traveler wires between the 3 way switches.
And why the 2- 3 way switches had a red and black on the brass screws.
What have now is the last switch has the white connected tot he black wire now.
That loops the power all the way back to the #1 switch.
You have no neutral in any of the boxes except maybe the bedroom where you have a fan on a circuit (is it the same circuit? if not, it is very dangerous).
If you disconnect all the wires in the Kitchen switch box, you will measure with a tester, one lead to the white in the 2 wire cable and one to ground and you will find it to be power.
I am surprised the Z waves have not blown as yet, they are very susceptible to mis wiring and fail all the time. 33% fail out of the box new.
If you can confirm the bedroom switch box with the fan switch, if it is on the same circuit breaker as this light on the Z waves, we can back feed the neutral all the way to take of the situation.
Use the tester and see what I have explained. Be sure there are no other wires not listed as that would change the entire situation, but as it is now, the switches are not wired properly and will burn out shortly.
See the diagram below to see how 3 ways are wired to the light with power originating at the light and not the switch.
This is how yours was wired except you have the 2 - 4 ways between the switches.