Is this 3 switch wiring arrangement allowed by code?
Better idea: use a part listed for the job to bypass the errant current around the lights
Fortunately, there's a way to bypass the errant &quot;phantom&quot; current (from capacitive coupling through the parallel traveler wires) back to neutral without doing anything that'd void your insurance.  Simply nut a Lutron LUT-MLC in between switched-hot and neutral at the first light fixture on the circuit; they're listed (as an appliance control) for use in mains wiring, so there's no need to worry about your insurance complaining.
As to your original idea...
While your original idea seems sound, it falls into a grey area of Code interpretation regarding the meaning of NEC 404.2(A), which was originally put in to prohibit dangerous Carter 3-way setups:

(A) Three-Way and Four-Way Switches. Three-way and four-way switches shall be wired so that all switching is done only in
the ungrounded circuit conductor. Where in metal raceways or
metal-armored cables, wiring between switches and outlets shall
be in accordance with 300.20(A).

In your case, neutral is never broken by any switch (breaking the neutral with a multiway switch also violates NEC 404.2(B)), but simply connected to an otherwise floating traveler wire to short out a voltage that got coupled over by a parasitic capacitor.  Note that this configuration doesn't parallel the neutral either, because the neutral-connected traveler and the actual neutral are connected to opposite sides of the load, which means that the normal issues with wires in parallel and NEC 310.10(H) don't apply here.