I'll echo what Tetsujin said with a bit more detail. At the end of the day, 40 ft, by 100ft is not a big space, when it comes to PA systems. The big thing you are looking for with any run in this length is simply to avoid picking up noise.
Sending a low power signal through any length of wire, unbalanced, will result in significant noise being picked up, however, if you are using a balanced signal with amps that are supporting a balanced input, then you can easily send the signal from the back of the church to the front without issue. If you have any instruments or vocals for worship, you'll already be sending much lower power balanced signals that far to get to the board anyway.
If you don't have balanced cables (TRS for your 1604) or your amps don't support balanced input, then you'll certainly want to put the amp in the back and send the powered lines to the speakers in the front.
Otherwise, you have your choice of options. Having the amp in the front will mean a bit less attenuation, but ultimately, you are not talking about a long run here. Keeping it in the back has the advantage of being able to easily reach it for troubleshooting if something goes wrong during a service.
If you can share more about the relative concerns of the two groups, that might help give more direct feedback as well.
Personally, at my church, which had roughly similar dimensions to yours, though we were setup for a wide room rather than a long one, we used the amps up front and sent a balanced signal, though a few years back, we redid the whole system to a digital board with a digital snake, so now everything is up on stage and we just have a network cable that connects back to the sound board.