I have an old model IPAC4 that I used back in 2008 running Win98, XP, etc. and I eventually rebuilt my system around the PI (you can see details linked in my profile or signature below). Anyway, my IPAC has the PS2 connector but works with a USB adapter cable.
Here is the thing--the IPAC is a keyboard. Or at least it looks like one to the computer to which it is connected. Your joysticks, assuming they are microswitch-based, could be pushbuttons. There is nothing about the fact that it is a stick vs. a button--it is simply shorting the input on the IPAC to ground.
So, what happens if you wired a joystick to BUTTON1,2,3,4 on the IPAC? I would think this would let you trigger those buttons when you move the stick to short the respective inputs. If true, you should conversely be able to wire a button to one of the joystick inputs and pressing the button should trigger that key. And this brings me to my point. . . Do you know what keyboard keys are getting sent by each directional trigger? How are you testing on the Pi? Are you opening a text file in Pixel for example? My player 1 joystick maps to the arrow keys I think. So, if I open a text fine on the Pi, I can move the cursor around just like I am typing arrow keys.
I know I am not offering an answer but more of a testing method. Mapping keys can get really confusing once you launch an emulator, so my approach is to verify the raw inputs are getting out of the IPAC and into the Pi.
One approach to testing keyboard inputs is to launch the keyboard testing executable from AdvanceMAME at commandline. This will let you watch on screen what the PI is receiving when you pound on buttons or move your sticks. I don't remember the test command off-hand, but if you dig into the Docs here on the RetroPie and look for the Spinners/Trackball page, there is a similar test you can run for Mouse input. I know, we are not testing a mouse, but there are three executables in there for AdvanceMAME that let you test each Mouse, Joy and keyboard inputs. Might be worth a little time looking that up. Sorry , don't have my Pi handy to check.
My thought is that once you know the inputs are getting sent, you are no longer troubleshooting the IPAC, but rather the mapping. Knowing that much can go a long way to figuring out the next step.