On a Tyros 4, use

* A1 Fingered Mode (set split point at F#2)
* Full Keyboard Mode

Notes to play (with piano voice enabled) in LH:

F1 - C2 - E2 : Dm7(9)
F1 - B1 - E2 : G7(13)
E1 - A1 - D2 : C6(9)

F1 - G1 - Bb1 - D2: Gm7
E1 - Bb1 - D2: C7(9)
E1 - F1 - A1 - C2: FM7

Eb1 - A1 - D2: F7(13)

It's been a while since I've played a PA2X,
but I got the same/similar chord recognition results playing the Pa2X in 'full keyboard' mode.
Not sure if any of the PA2X's fingered modes recognized this or not. Perhaps you can check these and report back.
Also, Make sure the latest current OS is installed on both keyboards.

John, looking forward to the results of your findings.