Hey Roy,
Being able to run pro sound is one of my curse/blessings. I have never used a feedback eliminator because they basically do what you can do with your board and a good EQ. The first factor is like you said, getting the singer to keep the mic close to their mouth. The second factor like you said is teaching then to keep their back to the speaker. The third factor is the overall volume and the fourth factor is finding the frequenccy that is giving you feedback and turning it down on the main EQ.
Here is something you can do that will help. When you get set up, run a sound check. Have somebody stand in the worst place with the mic open and turn the overall (main) volume up some. This will kick up the feedback. Once the feedback is ringing, start pulling down the EQ faders on your main EQ (32 band if possible). When You find the frequency that is causing the feedback pull that fader down and pull the faders on either side of it down just a bit. After this is done you should be able to turn the main volume down to a resonable level and make your EQ adjustments on the channel EQ's to tweek it in. By doing this you are doing what the feedback eliminator does. Oh, when folks hear the feedback, be sure to announce that they are all now sterile. This always gets a chuckle.
I Hope This Helps
Jim