While not basing the OS on POSIX is good, if you ever want to use it for more than a hobby, i.e. if you ever want to use it for your main personal computer, you will also need a translation layer for the LINUX syscalls, which would enable you to compile and run any of the existing open-source programs, or even run existing binaries.
Porting the programs that you are more interested in from Linux or *BSD to your own OS is the best, but this is necessarily slow and also the work of porting rarely used applications may not be worthwhile.
An alternative to a syscall translation layer is for your OS to act as a hypervisor for Linux or other OSes VMs. However, this would have a lower performance than using natively your IPC-based OS.
Porting the programs that you are more interested in from Linux or *BSD to your own OS is the best, but this is necessarily slow and also the work of porting rarely used applications may not be worthwhile.
An alternative to a syscall translation layer is for your OS to act as a hypervisor for Linux or other OSes VMs. However, this would have a lower performance than using natively your IPC-based OS.