I agree with @FuzzyBoots that the "Effing" stands for "fucking".
However, I think the whole phrase is a little deeper/cleverer than just the fucking (something, something, unskilled labour...).
The "Cranks" part is using the slang definition to mean a person with unusual, often crazy ideas. But, it is also being used in the phrase to mean some device that creates movement between two parts of a machine (e.g. he turned the crank to start the car engine). In the context of what the CET is trying to achieve, they would be tweaking all the religions to fit into one - cranking the words to get them to fit.
The "turners" bit is the plural of "crank turner" (i.e. turners). These are the people (plural) turning the crank to get the cohesion between the religions and by inference influencing the belief system of the universe. In the context of Dune, this would be the manipulation of the populace by religion/belief systems and these are the people turning the crank to get people to believe what they say is canonical. You could also say something similar about the Bene Gesserit being the people turning the crank to get the end that they want.
An alternative interpretation of the the "brown repose" part is that these CETers are all people of esoteric knowledge, perhaps so highly specialized that they might consider themselves to be the only one to understand their logic/reasoning or all the intricacies of the problem. People who are like this are prone to "brown study" or contemplation of their own thoughts - so might appear lazy (insert joke about mathematicians needing only wastepaper basket and philosophers not even needing that...). Adapting brown study to brown repose (given the location in Hawaii) doesn't seem like a big stretch to me.