Can you just replace "it was not until" with "it was only after"? Yes, those two phrasings are close enough in meaning and structure that the difference hardly matters. Let's not worry quite yet about whether the two events in question could happen at the same time.
Are any further changes needed? No. In fact, that change isn't needed. The sentence is fine as originally presented.
Can you rewrite it as "It was not until the government stepped in and requested that the oil company reroute the pipeline agreed the corporation to honor the wishes of the protestors"? No. The original sentence has a structure:
It wasn't until [a certain time] that [something happened].
That first piece doesn't even need to be a clause. It can be, and it certainly is in the original sentence. Another sentence might use a different time referent, like "It wasn't until Tuesday that the package finally arrived."*
That second piece is a clause. That "that" introducing and subordinating the clause is not optional here. There isn't anything about the sentence's overall structure that justifies inverting the subordinate subject and verb.
The overall structure does involve something a little bit like an inversion. It's an it-cleft sentence. Without that cleft structure, we're left with something like this:
The corporation did not agree to honor the wishes of the protestors until the government stepped in and requested that the oil company reroute the pipeline.
The it-cleft of the original sentence has a subject/verb pairing of its own: it/was. That's different than the sort of inversion that you mentioned in a comment below SoronelHaetir's answer.
Not until liberation did he return.
It wasn't until liberation that he returned.
The former sentence contains one clause, and its structure requires the subject/auxiliary inversion. The latter contains two clauses, and neither clause admits any subject/verb inversion.
* Tuesday's package suggests that we might need to consider whether two things happen at the same time. Reading the TEFL sentence, I expect the corporation agreed after the government stepped in. Reading my own sentence, I expect the package arrived on Tuesday. The difference between "not until" and "only after" becomes clear somewhere between Tuesday and Wednesday.