There are several possibilities for the reversed cell, depending on the flashlight design.
The first is the flashlight is designed as you'd expect, takes power from the battery of 3xAAA as you'd expect, and works well from 4.5v to a very low voltage.
If you take 3 random batteries, even new ones, they will be slightly mismatched. If you connect them in series, and run them down, then one of them will be more 'run down' than the others. If you run them down far enough, the weakest will be reversed by the other two.
How far do you need to run them down? If the flashlight fails at 4v, chances are you don't get a reversal. If it fails at 2v, you probably will. If your problem that the flashlight keeps going and works too well at low voltage?
You may just have been unlucky, and got a bad mix of cells, 2 out of 2 is not out of the realms of possibility. Try again with a fresh set of cells.
The other (remote) possibility is that the flashlight taps off an intermediate battery connection for bias or something, and so hammers one cell harder than the others. You opened another flashlight, was the reversed battery in the same position? If yes, that supports this possibility. If not, then it refutes it.
With care, you can fashion a probe to measure cell current in situ, ideally with a scrap of copper clad PCB, but you might be able to make something with an old credit card, tape and some foil. See if the running currents from each cell are equal.
Spring battery holders are notorious for poor contacts, corrosion at the contact point between cell and spring, and moving the cell around in the holder is the 'standard' way to get the contact made again. This issue is completely independent of the cell reversal issue.
Yes to caveats. The common mode choke is not magic, being instead one leg of a voltage divider. The common mode chock is the series element of the divider.
You need to provide a shunt element, for the choke to be effective. You can explore several shunting methods
(1) shunt between the +/- pairs only
(2) shunt from each of the differential wires to GND/RETURN
(3) combining 1 & 2
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SMD choke rated for 50V 0.3A must have a critical solder profile followed exactly to prevent insulation failure