Top Law Schools

So I will be applying to T14 law schools this cycle, and am contemplating whether it would be better for me to take the GRE over the LSAT. My dilemma is that while I do have a beautiful 4.03 CAS GPA from UCLA, I have always been really bad with standardized tests, and for the past few months I have been studying for the LSAT, took dozens of timed preptests, and even took the July 2019 official LSAT (which I received a 156 and cancelled). I have not been able to score higher than a 163 on any timed LSAT preptest, and given my bad history with standardized tests (like the SAT), I am 100% certain that If I were to take the LSAT again, it would be below the median score at every T14 law school, thus making me a Reverse-Splitter.

I realized then that since law schools are not required to report the GRE scores of applicants who only took the GRE, would this mean that law schools would be more likely to admit me if I applied with my 4.03 GPA and a mediocre GRE score rather than a 4.03 GPA and a 163 LSAT since they wouldn't be required to report my GRE score thus allowing them to boost their GPA median while at the same time taking no hit to their LSAT median?

Is it a good idea for a potential Reverse Splitter like myself to take only the GRE in order to boost my admission chances?

There is no such thing as a reverse splitter; there are only students who need to buckle down on the LSAT.

No, this won't help your chances. You can see if you'll perform better in the GRE, but you need to get a competitive score on either test to have a good shot at top schools.