PS1 DualShock pad breaks between 4.3 and 4.4+

[MagNeato]

A Playstation 1 DualShock controller plus an Amazon USB adapter works well in RetroPie 4.3.
The same setup in 4.4 behaves differently; most obviously, jstest reports less buttons and the "X", "Square" and "O" buttons do not work. It's broken in the same way in RetroPie 4.5.1; the pad is recognized as a PS3 controller just like in 4.3, but the "Configuring" dialogue in the recalbox GUI can't be completed because the SNES equivalents, A, B and Y don't register button presses.

What can I do to get the old behavior back in 4.4+ ?

The jstest output in 4.3 shows:
   "..and 19 buttons"
4.4 only shows:
   "..and 13 buttons"

4.3 command output:

pi@retropie:~ $ lsusb
Bus 001 Device 005: ID 054c:0268 Sony Corp. Batoh Device / PlayStation 3 Controller

pi@retropie:~ $ jstest --event /dev/input/js0
Driver version is 2.1.0.
Joystick (Sony PLAYSTATION(R)3 Controller) has 27 axes (X, Y, Z, Rz, (null), (null), (null), (null), (null), (null), (null), (null), (null), (null), (null), (null), (null), (null), (null), (null), (null), (null), (null), (null), (null), (null), (null))
and 19 buttons (Trigger, ThumbBtn, ThumbBtn2, TopBtn, TopBtn2, PinkieBtn, BaseBtn, BaseBtn2, BaseBtn3, BaseBtn4, BaseBtn5, BaseBtn6, BtnDead, BtnA, BtnB, BtnC, (null), (null), (null)).
Testing ... (interrupt to exit)
Event: type 129, time 3037500, number 0, value 0
Event: type 129, time 3037500, number 2, value 0
Event: type 129, time 3037500, number 3, value 0
Event: type 129, time 3037500, number 4, value 0
Event: type 129, time 3037500, number 5, value 0
Event: type 129, time 3037500, number 6, value 0
Event: type 129, time 3037500, number 7, value 0
Event: type 129, time 3037500, number 8, value 0
Event: type 129, time 3037500, number 9, value 0
Event: type 129, time 3037500, number 10, value 0
Event: type 129, time 3037500, number 11, value 0
Event: type 129, time 3037500, number 12, value 0
Event: type 129, time 3037500, number 13, value 0
Event: type 129, time 3037500, number 14, value 0
Event: type 129, time 3037500, number 15, value 0
Event: type 129, time 3037500, number 16, value 0
Event: type 129, time 3037500, number 17, value 0
Event: type 129, time 3037500, number 18, value 0
Event: type 130, time 3037500, number 0, value 0
Event: type 130, time 3037500, number 2, value 0
Event: type 130, time 3037500, number 3, value 0
Event: type 130, time 3037500, number 4, value -32767
Event: type 130, time 3037500, number 5, value -32767
Event: type 130, time 3037500, number 6, value -32767
Event: type 130, time 3037500, number 7, value -32767
Event: type 130, time 3037500, number 8, value -32767
Event: type 130, time 3037500, number 9, value -32767
Event: type 130, time 3037500, number 10, value -32767
Event: type 130, time 3037500, number 11, value -32767
Event: type 130, time 3037500, number 12, value -32767
Event: type 130, time 3037500, number 13, value -32767
Event: type 130, time 3037500, number 14, value -32767
Event: type 130, time 3037500, number 15, value -32767
Event: type 130, time 3037500, number 16, value -32767
Event: type 130, time 3037500, number 17, value -32767
Event: type 130, time 3037500, number 18, value -32767
Event: type 130, time 3037500, number 19, value -32767
Event: type 130, time 3037500, number 20, value -32767
Event: type 130, time 3037500, number 21, value -32767
Event: type 130, time 3037500, number 22, value -32767
Event: type 130, time 3037500, number 23, value -32767
Event: type 130, time 3037500, number 24, value -32767
Event: type 130, time 3037500, number 25, value -32767
Event: type 130, time 3037500, number 26, value 0

If I press the X,Sq,O,Tr face buttons:

Event: type 1, time 3053960, number 14, value 1
Event: type 1, time 3054110, number 14, value 0
Event: type 1, time 3056260, number 15, value 1
Event: type 1, time 3056390, number 15, value 0
Event: type 1, time 3058710, number 13, value 1
Event: type 1, time 3059050, number 13, value 0
Event: type 1, time 3057450, number 12, value 1
Event: type 1, time 3057790, number 12, value 0

4.4 command output:

pi@retropie:~ $ lsusb
Bus 001 Device 005: ID 054c:0268 Sony Corp. Batoh Device / PlayStation 3 Controller

pi@retropie:~ $ jstest --event /dev/input/js0
Driver version is 2.1.0.
Joystick (Sony PLAYSTATION(R)3 Controller) has 6 axes (X, Y, Z, Rx, Ry, Rz)
and 13 buttons (BtnX, BtnTL, BtnTR, BtnTL2, BtnTR2, BtnSelect, BtnStart, BtnThumbL, BtnThumbR, (null), (null), (null), (null)).
Testing ... (interrupt to exit)
Event: type 129, time -46530, number 0, value 0
Event: type 129, time -46530, number 1, value 0
Event: type 129, time -46530, number 2, value 0
Event: type 129, time -46530, number 3, value 0
Event: type 129, time -46530, number 4, value 0
Event: type 129, time -46530, number 5, value 0
Event: type 129, time -46530, number 6, value 0
Event: type 129, time -46530, number 7, value 0
Event: type 129, time -46530, number 8, value 0
Event: type 129, time -46530, number 9, value 0
Event: type 129, time -46530, number 10, value 0
Event: type 129, time -46530, number 11, value 0
Event: type 129, time -46530, number 12, value 0
Event: type 130, time -46530, number 0, value 0
Event: type 130, time -46530, number 1, value 0
Event: type 130, time -46530, number 2, value -32767
Event: type 130, time -46530, number 3, value 0
Event: type 130, time -46530, number 4, value 0
Event: type 130, time -46530, number 5, value -32767
Event: type 2, time -42260, number 0, value 675
Event: type 2, time -42240, number 0, value 0

If I press the X,Sq,O,Tr face buttons (only Tr registers a press, and number is "0" instead of "12"):

Event: type 1, time -40110, number 0, value 1
Event: type 1, time -39960, number 0, value 0

This is the adapter I'm using: Mcbazel PlayStation 2 Controller to USB Adapter for PC or Playstation 3 Converter Cable for Sony DualShock PS2 PS3 Controllers (NOT compatible with Dancing Mat Guitar Hero) - https://smile.amazon.com/gp/product/B000NJBD90/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1