So it's a 147' deep by 65' wide room with a 9'-10' ceiling and the system is used primarily for speech. I can see why the existing system is problematic and this sounds like a great application for a distributed system.
With the relatively large room you probably have to have the front speakers quite loud to get sound to the back. However, the low ceiling prevents you from getting them up higher to where you can get good coverage of the room and almost certainly results in a lot of sound hitting the ceiling and rear wall. This system was probably way down in level and had poor intelligibility further back in the room. Based on what I've seen elsewhere, the rear speakers were quite likely an attempt to address this, but just as in almost all of those other cases, ended up causing as many or more problems than they solved.
It also seems that you have primarily mono sources but a stereo (and with the rear speakers almost a quadraphonic) configuration, meaning that you have the same signal coming from multiple speakers. This results in all sorts of interactions in the listening space as at any one point the listener is getting the same signal from four different sources but with the four signals arriving at different times and with different levels. These timing and level relationships differ at every point, meaning you get different interactions everywhere, some of which may be rather undesired. For speech, in some ways you may actually be better to have it come from just one speaker.
A distributed system uses many small speakers distributed throughout the space with each speaker covering a small are. This places the listeners closer to the speakers and allows the sound from the speakers to directed at the listeners rather than at where they aren't. This can not only reduce the levels and echoes on the stage, and thus help address your feedback issues, but could also improve intelligibility so that people better understand what is said.
Unfortunately, many people seem to look down on distributed systems, perhaps seeing them as old technology or relating them to inexpensive installations they've seen. However, none of the physics involved has changed and with some of the current processing and high quality ceiling or small speakers available, they can be very effective. If you want to get real fancy, and have the budget, you could even look at a distributed system with electronic acoustical enhancement systems (LARES, LCS VRAS/Meyer Constellation. ERES, etc.) that can help emulate different acoustical environments, letting the space sound like a lecture hall or a cathedral at the push of a button.
Another alternative would be to use one of the steerable arrays that are now available. such as the Duran Audio Intellivox or Renkus-Heinz Iconyx. These use advanced digital processing to control and steer the speaker's vertical coverage, in some cases into a very tightly defined pattern that can help keep the sound aimed at the audience.
If you don't have a large budget then I would guess that a properly designed and installed distributed system might be the best approach for this application.
With the relatively large room you probably have to have the front speakers quite loud to get sound to the back. However, the low ceiling prevents you from getting them up higher to where you can get good coverage of the room and almost certainly results in a lot of sound hitting the ceiling and rear wall. This system was probably way down in level and had poor intelligibility further back in the room. Based on what I've seen elsewhere, the rear speakers were quite likely an attempt to address this, but just as in almost all of those other cases, ended up causing as many or more problems than they solved.
It also seems that you have primarily mono sources but a stereo (and with the rear speakers almost a quadraphonic) configuration, meaning that you have the same signal coming from multiple speakers. This results in all sorts of interactions in the listening space as at any one point the listener is getting the same signal from four different sources but with the four signals arriving at different times and with different levels. These timing and level relationships differ at every point, meaning you get different interactions everywhere, some of which may be rather undesired. For speech, in some ways you may actually be better to have it come from just one speaker.
A distributed system uses many small speakers distributed throughout the space with each speaker covering a small are. This places the listeners closer to the speakers and allows the sound from the speakers to directed at the listeners rather than at where they aren't. This can not only reduce the levels and echoes on the stage, and thus help address your feedback issues, but could also improve intelligibility so that people better understand what is said.
Unfortunately, many people seem to look down on distributed systems, perhaps seeing them as old technology or relating them to inexpensive installations they've seen. However, none of the physics involved has changed and with some of the current processing and high quality ceiling or small speakers available, they can be very effective. If you want to get real fancy, and have the budget, you could even look at a distributed system with electronic acoustical enhancement systems (LARES, LCS VRAS/Meyer Constellation. ERES, etc.) that can help emulate different acoustical environments, letting the space sound like a lecture hall or a cathedral at the push of a button.
Another alternative would be to use one of the steerable arrays that are now available. such as the Duran Audio Intellivox or Renkus-Heinz Iconyx. These use advanced digital processing to control and steer the speaker's vertical coverage, in some cases into a very tightly defined pattern that can help keep the sound aimed at the audience.
If you don't have a large budget then I would guess that a properly designed and installed distributed system might be the best approach for this application.
And..... I'll turn up the front speakers 
