GRE

The GRE is a measurement tool, not a performance. Taking a GRE subject exam that you don't need Mike to communicate the wrong things to an application review committee. It might appear that you would prefer to study the area covered by your subject exam. It might look like you are trying to gain entry on the basis of the ability to test well, without the ability to perform well academically. If possible, it would be much better to demonstrate academic prowess by taking some courses as a postbacc. Failing that, it should be obvious which GRE subject exam you should take: chemistry for chemical engineering, or physics for electrical engineering or mechanical engineering. However, I doubt that this approach will solve your problem, and it may make things worse.