NXP arm microprocessor memory erase - no JTAG
THE OBVIOUS METHOD is to use the built in bootloader and [flashmagic] to erase it via the serial port. I'm guessing that you already considered and rejected this method, possibly because your board doesn't give you access to both the serial port pins and the boot control pin(s). The LPC2368 overview suggests the bootloader also works via USB. I didn't confirm.
THE TIMING METHOD: (Part of) the reason you can't get control via JTAG is that the aforementioned system bootloader always1 runs after reset, no matter what the boot pin settings, and JTAG cannot get control until after that is finished. What you need (after a hardware reset) is for the JTAG controller to assert [TMS, I think] just after the system bootloader is finished, but before your code changes the problematic registers. If you keep trying to connect via JTAG, with random timing between that and your hardware reset button, you might fail 500 times and get lucky on the 501st.


Note 1: It has to run at least far enough to verify your "magic checksum"

Note 2: This would be better as a comment but I don't have rep points.