I know that students from Yale, Harvard, Stanford etc will often say SLS/YLS/HLS and it's totally acceptable. What I did was I would spell it out the first time, then use the abbreviations for any following reference.
... BLACK LETTER LAW: Use the supplements. Anything will do; your professor ... will allow you access to supplements (Lexis Summaries, Quimbee, CALI, BARBRI ...
... like Yale (61%), Harvard (57%), Stanford (50%), and Chicago (61%) -- or ... like Yale (61%), Harvard (57%), Stanford (50%), and Chicago (61%) -- or ...
I took the January 2015 LSAT (might have been Feb?) and used it to be accepted to T14s that cycle. The only school that wouldn’t accept the score was Stanford. Good luck and I hope that helps!
I think it’s a good idea. One of the admissions reps at Stanford called it a miss opportunity to not do the optional essays (aside from the diversity one, which depends on your circumstance).
... written for that school, so Stanford is just making a point ... you want to go to Stanford in your PS. But, yes ... any kind, including a why Stanford essay. The only exception would ... you want to go to Stanford.