Vic,
In a normal wye configuration, the wiring is pretty easy - the 2 ports named "out" on the AR1 go to the straight leg end of the wye turnout and the 2 ports named "in" go to the straight leg end of one of the turnouts (either LH or RH) leading into the wye, and the turnouts are isolated from the curved tracks within the actual wye. Really quite simple ... once you see the diagram.
You want to wire back-to-back wyes, attached directly to each other as wye turnout "A"'s straight leg attached directly to wye turnout "B"'s straight leg... and I don't know if this can be done; I know of no case where this has been done in your configuration. One can wire 2 "reversing loops" back-to-back with sufficiently long straight track between the 2 wye turnouts. But one needs to break that straight track into separate distinct pieces (blocks) to create the necessary configuration. Here's a document from DCC Specialties regarding their PSX-AR reversing unit (
https://www.dccspecialties.com/products/pdf/man_psxar.pdf) that has a diagram on page 6 showing the configuration needed.
However you might not have 2 actual wyes, at least not 2 independent wyes; instead, this might be 2 wyes superimposed on each other. And if that is the case, that is not electrically possible. Someone with far more wiring knowledge than I have needs to advise on this.
The prior version with the crossover was actually 2 independent reversing sections, and may be your better option ... except for the derailment shorting problem ... I think. If you are well-versed in electronics, or get the right equipment to wire in, the crossover version would work if both paths of the crossover were normally not powered, and only once a train entered one side/path of the crossover would that path be powered, making sure that both paths could not be powered at the same time. You'd have 2 reversing sections and 2 AR1 devices, but each would meet the independence requirement.
So the option for having the crossover powered only when the train is using it becomes ... what?
I'm not a Kato user, so I don't speak to the capabilities of Kato track. But what might be a simple way is to have power to the crossover path come only via the turnout leg used to enter that path. That's a little tricky and an interesting wiring problem because the turnout leg at the other end of that crossover path can't be supplying power concurrently, as it would then be creating a short. Meaning that when the power reverses within the crossover path, the power stops coming (cut off) from the entering end and is then coming from (logically turned on at) the exiting end. Probably means in reality that, once the power is reversed within the path, that the entering turnout is automatically thrown to the "through" path and the entering leg of the turnout is logically disconnected power-wise while at the exiting end only then is the turnout thrown and power starts to enter from that end. Complicated to say the least. Must be done automatically. And almost instantaneously to keep the train moving. Meaning the complete train/last metal wheel set must clear the entering turnout before power is reversed to prevent shorts. And wiring in place to ensure that both entering and exiting turnouts cannot be aligned for the crossover path at the same time. It's complex wiring and complicated to install, but I believe I could do it for the track I use (Peco) and turnouts using Tortoise motors wired together to effectively operate as one logical motor; the double-motor wiring as one logical motor is just a version of double-slip wiring. Can one do this with the Kato track you use? I don't know. Probably. Maybe.
So if this is possible, this could be your solution.
Or your worst nightmare.