Your machine should definitely be able to run APEO and the APEOed executable without problems.
I don't have AmigaOS 3.2.x, so I can't make tests on that OS.
The fact that you get a crash when passing no arguments is suspicious - you should get this message, instead:
APEO
ERROR: could not parse command line or bad arguments.
Could you try to run APEO without arguments after booting without startup-sequence and see what happens, please?
Also, could you send me by email (contact@retream.com) your program original executable? I would process it for you and send the APEOed executable to you, so that you can see whether it works or crashes.
EDIT: also, please try the new version I have just uploaded, as it fixes a major bug that might well be the cause of your headaches (this was due to the fact that Hex$() produces always the shortest string possible, whereas at a specific point the code needed exactly 8 characters - see the history log for the details regarding what ensued).