I Was told to get the EFSET test from a company abroad and send the certificate to evaluate my English level. So I would say that it has some power. In fact, its a good test and very reliable if you are serious IMO.
I'm going to guess that it will be difficult, depending on what you mean by a "top university". Your CE background has some math, it is true, but you are probably missing quite a few of the courses that math graduates will have had.
The math subject test itself is very difficult and tries to cover many topics. Even a math graduate will have had no courses ...
I worked in the admissions office of the graduate school of arts and sciences at Harvard University.
While the GRE is important, there are a kaleidoscope of other factors that admissions takes into consideration.
You stated, quite eloquently, what happened, which was that you were so engaged in research that it hurt your study time for the GRE.