Some searching and some trial and error later I find that adding a "reboot=p" to the kernel command line will result in en rebootable system. It looks like this system ("HP t640 Thin Client") should be added to the list of boot quirks in 'arch/x86/kernel/reboot.c'?
For the record, "c,p", "g,p" and "p" work, all other combinations fail to do a functional reboot.