I've never tried to do that with group policy. Something new to me. Group policy works on Pro systems not just servers but not one crappy Home systems, where it is nobbled intentionally.
The scheduled task thing is an excellent idea. It would presumably quit when you log out though. If you can set up the service thing successfully, and that is indeed an ‘if’, then that is the way to go.
If all else fails, could always consider running it in a VM, and inside the VM just have it auto-start when the VM boots, then it only remains to choose a convenient way of starting up the VM instance itself. I only suggest this kludge because it might be a way of getting round the service hardening thing, restrictions on the types of operations allowed. But then we have the same question about the VM executable and whether it is service-friendly. This is a nasty plan.