If you get paid in money in service to the Church, you are doing precisely the same thing as any of us that are paid in money, you are working for it, you are getting wages for your work. Your work makes you no better than those that, for instance, feed you by growing food for you to spend your wages on.
Yes I quite agree with you here. As I see it, the issue was never about work. It was about our motives; why we work. Work for love vs work for money. Whether it's evangelism, pastoring, discipling or plumbing, architecture, or being a janitor; the deciding factor is the motivation for why all those people choose to work. Do they work for love or do they work for money? That is the point Jesus made about the two masters; God or money.
As for the distinction between work and serve, I think you've again misunderstood the verse in question. Let us pretend, just for the sake of this example, that your original assumption was correct and Jesus was referring to the two masters as God and Satan. Would your distinction still make a difference? Imagine claiming that it's fine to work for Satan as long as you're not serving him. This is what you've done in the case of mammon, but because mammon includes things like money and material necessities, you've somehow seen "serve" and "work" in a different way. If you are willing to claim there is a difference between serving and working for Satan, I still won't agree with your assessment, but at least I'll know that your reasoning is consistent.
Where would you be without the farmer? ...one of the very people you suddenly got shy about saying they work for/serve mammon because they aren't in service of the Church.
Working for love IS the work of the church, whether it's farming or whatever. But as for the question of "where would you be without the farmer" I think the same answer Jesus gave to Satan is appropriate here, too; "man does not live by bread alone" (Matthew 4:4). If your faith is in the farmer, or anyone because of what they can do (or not do) for you materially, then how will you ever be able to lay your life down?
The farmer works for a wage but that in itself doesn't mean they "work for" as you put it or "serve" mammon.
We're all taught from birth that money makes the world go round. Very few of us get any kind of alternative influence. We're taught not only to depend on money but that money will bring a more happy and comfortable life. Food comes from money (where would we be without the farmer who works for wages, right?). Clothing comes from money. Everything comes from money. We are saturated in it to the point that most of us genuinely believe that we'd die without it. But really think on that for a moment; is it true that humanity would die without money? Because God is the giver of life, he is the only thing in this existence that we cannot live without and yet somehow we've come to see it as mammon instead.
The majority of the world operates on a "fiat" system, meaning that the money we use is not backed up by any physical wealth. Money only has as much value as we choose to believe it has. The money itself does nothing. It does not work or produce. It simply acts as a system to manipulate people into working. This is why motivation (rather than the money or the work itself) is so important. Money only exists because people choose to believe it is necessary. Money is not life or death. It is a choice.
Sometimes that choice is not a result of rational, critical thought, but rather the product of years of indoctrination. When someone comes along saying, "hey, why not just work for each other rather than for little bits of paper and metal" they sound like oddballs, not because the ideal really is odd, but because it's so different from what the person has been taught to see as normal. Working for money is normal. Working for love is oddball. This is why "friendship with the world is enmity with God". (James 4:4)
I personally believe this is what Paul was referring to when he talked about the carnally minded person who can't discern spiritual issues (1 Cor 2:14). I think it's why Jesus quoted Isiah when he said, "seeing they do not see and hearing they do not hear" (Matthew 13:14-15) and "this people draw near to me with their lips, but their heart is far from me" (Matthew 15:8). And it's why Jesus asked, "why do you call me Lord, but do not obey me" (Luke 6:46)?