Process: jd-gui 
Code Type: X86 (Native)
Parent Process: ??? 
Responsible: jd-gui 
User ID: 501
Date/Time: 2017-02-21 12:06:45.436 +1000
OS Version: Mac OS X 10.12.3 (16D32)
Report Version: 12
Anonymous UUID: FD4C197F-34C0-7E0B-A88A-B0BDD3397DD7
Sleep/Wake UUID: F6E62B43-7C66-4E90-8968-E92535403845
Time Awake Since Boot: 700000 seconds
Time Since Wake: 320000 seconds
System Integrity Protection: enabled
Crashed Thread: Unknown
Exception Type: EXC_BAD_ACCESS (SIGSEGV)
Exception Codes: KERN_INVALID_ADDRESS at 0x00000000241499f5
Exception Note: EXC_CORPSE_NOTIFY
Termination Signal: Segmentation fault: 11
Termination Reason: Namespace SIGNAL, Code 0xb
Terminating Process: exc handler 
Fortunately there was a way to fix it! The latest version (1.4.0 at the time of writing) from the download page fixed the problem.
The latest DMG download also had the same error on launch as my original version, but the TAR download was ok. After doing some reading on the issue it looked to be a problem with JD-GUI needing to be recompiled on the latest Xcode.
I expect the real issue was with Launch4J needing to be updated to work with the latest macOS. Anyway after installing the new version it worked perfectly.