I think that you did not make a mistake with your assumption.
I did almost the same thing and is working without problems on both LPC2368 and
LPC2387. I have an old Keil uVision that does not support LPC2300. Therefore I
have set CPU as LPC2214, but with startup file for LPC2300 and of course a
suitable header file.
Maybe you have overwritten the bootloader code. You can try to communicate with
the bootloader using a terminal. The protocol is ASCII based and described in
the datasheet. That way you can find out exatcly where is the problem. An
alternative is to use a serial port monitor.