This is exactly what people always try first. They generally exhaust themselves dealing with this very issue. They buy more and more electronic equipment without ever getting the improvement they need until they’re finally ready to give up on the allure of electronics, sit down, and listen and learn about the world of acoustics.
Acoustics is a whole world, invisible to the eye, but very audible to the ear. Once the sound is launched in the air, only acoustics can help guide it to where it is supposed to go. That’s what we do at ASC. We take over where the electronics leave off. Here is how we work: we get photos, floor plans, elevations, descriptions of the problem, and often times audio recordings from you. Then we estimate the probable cost for the “fix” for your particular situation. Now you have a budget to talk about. Once you decide that your ready to start working to fix the problem, we analyze the problem in detail, design and build the solution and you install it. You get to skip the middle man by purchasing the proper solution direct from the factory.
We can also work with your audio technician, train them to do the testing we need to analyze the room, provide appropriate photos, and conduct interviews. We do our homework before we invest any time in working up a design. We have to know what the rules are within the church so we can work within those guidelines.
To answer some of your specific concerns, you should know that it is the echoes that create feedback. Sound technicians are always fighting “gain before feedback”. Improving the on-stage acoustics is one way to improve this. Eliminating echoes also helps to improve the mic problems. Of course, it is always a good idea to first check to make sure the sound system is set up properly and not aimed directly at the microphones. Beyond this, it is the acoustics that can make the necessary improvements.