On Debian we use the start-stop-daemon utility, which handles pid-files, changing the user, putting the daemon into background and much more.
I’m not familiar with RedHat, but the daemon utility that you are already using (which is defined in /etc/init.d/functions, btw.) is mentioned everywhere as the equivalent to start-stop-daemon, so either it can also change the uid of your program, or the way you do it is already the correct one.
If you look around the net, there are several ready-made wrappers that you can use. Some may even be already packaged in RedHat. Have a look at daemonize, for example.