Using a kernel exploit to gain higher privileges is likely to be successful if you've identified that the kernel on the target system is unpatched and vulnerable. Kernel exploits can provide the highest level of system access, often bypassing security mechanisms and giving the attacker full control over the system. In this scenario, exploiting the unpatched Windows Kernel vulnerability is a direct and effective method for privilege escalation to NT AUTHORITY\SYSTEM. Changing group policy settings or installing unauthorized software would generally require administrator-level privileges to begin with and would thus not be feasible from a limited shell access. Although buffer overflow vulnerabilities can lead to privilege escalation, they are not directly related to the kernel vulnerability in this context, making the kernel exploit the more appropriate choice.