I'm sorry that I don't have the technical language to explain this more clearly, but the following are the only two grammatically correct ways to say this phrase: "Only if that task were accomplished would it be possible to cope..." This is the passive voice, stylistically. "It would only be possible to cope if that task were accomplished..." This is the active voice. In the United States, we have been taught over the last several decades that the passive voice should be avoided, but if you look at literature from before 1960 or so, you will see it everywhere, because it was considered the "more formal" way to write.

It's 2nd conditional, so it must be past indefinite in the conditional part and would + infinitive in the main, "will" is grammatically wrong. The inversions is used for emphasis, for stylistic purpose.

To me would it be sounds more of a rhetorical question. Will it be sound slike you actually need a response .

'is direct order in this case will be correct' - what do you mean?? :) oh, you mean 'the other way around'.. but are you also asking about 'will' and 'would'?