It would be more like "Cochrane almost got it but would never have made the thing really work, and each iteration of future engineers did the necessary work to get the thing warp-borne". It would then follow that each successive iteration would have to do less work than the previous one and could rely more on historical records of how the first warp engine "was" designed and built.And wouldn't this require many engineers to come back to Zef's workshop immediately after the Borg attack, each doing a little bit of the work? So until the time that they actually complete a working ship, first contact never happens, and Earth gets assimilated?
For example, the original ship could lack the helical field shunt altogether. The first shanghaied engineer would improvise one from available junk, as well as create a missing cuboid countersink; the second one would read from the history books that Cochrane had used mystium-coated bedsprings for the helical field shunt, and would do exactly that, plus solve the problem of the missing cuboid countersink a bit more elegantly than the first one; and the third one would have the refined instructions for both the field shunt and the countersink and could concentrate on improving a third component.
Different timelines, though. For all we know, most of those other engineers were Geordi LaForge, just from a slightly different present.And also, if we had many different teams of engineers working on Zef's ship, why didn't we see the first team? After all, they were meant to be there at the same exact time as Geordi's team, weren't they?
Timo Saloniemi