You might still have a slight chance of taking advantage of a service if the service's executable DACL is well configured, and the service's binary path is rightly quoted. Should the service DACL (not the service's executable DACL) allow you to modify the configuration of a service, you will be able to reconfigure the service. This will allow you to point to any executable you need and run it with any account you prefer, including SYSTEM itself.
To check for a service DACL from the command line, you can use Accesschk from the Sysinternals suite.
accesschk64.exe -qlc thmservice

Here we can see that the BUILTIN\\Users group has the SERVICE_ALL_ACCESS permission, which means any user can reconfigure the service.
icacls C:\Users\thm-unpriv\rev-svc3.exe /grant Everyone:F

To change the service's associated executable and account, we can use the following command (mind the spaces after the equal signs when using sc.exe):
sc config THMService binPath= "C:\Users\thm-unpriv\rev-svc3.exe" obj= LocalSystem

Notice we can use any account to run the service. We chose LocalSystem as it is the highest privileged account available. To trigger our payload, all that rests is restarting the service: