There are demo examples.
https://www.nxp.com/webapp/Download?colCode=S32K3_HSE_DemoExamples
It is basically the same functionality as HSE DEMO ported to the code which is debugger independent. For instance if you use S32K344_HSE_FW_INSTALL, you may install HSE FW with using of any debugger.
I have tried it also with S32K312 device, if you create ticket I could send it to you:
https://www.nxp.com/support/support:SUPPORTHOME