I have been using OpenOCD successfully for NXP Kinetis and NXP LPC 8xxx devices. I have not used it with the LPC55Sxx series, and I don't have a LPC55S28. I do have a 55S59 and 55S16, so if time permits, I can try it out. But: OpenOCD is supported by the community, so the OpenOCD community would be the best place to ask for support. I know from my S59 and S16 that the flash architecture is very different, so it will require specific support for it from the OpenOCD community.
Somewhat related: I'm working on gdb server support with LinkServer (MCULink and MCULink-Pro) which gives you command line support/scripting/etc. This might be something for you too?