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In interviews with some of the adcoms of the schools I am applying to, they said that they would consider the average of multiple LSAT scores without an explanation for why to take the higher one. Most people have to explain an increase - I have to explain a decrease. Is this persuasive? If not, how might I got about it? Thanks.

Although I scored a 157 on the October 2010 administration of the LSAT I believe that the 160 I scored on the February 2010 administration better represents my ability and my potential to succeed in law school. I chose to retake the LSAT because I felt that I could improve upon my score of 160 and thought that my lower-than-expected performance was due to a missed inference on one part of the Analytical Reasoning section. I began to prepare again in June, but devoting the time necessary to improve upon my previous score became increasingly difficult once I gained full-time employment. I believe that the added pressure that came with this dual time commitment was why my score dropped three points.

This isn't persuasive at all. You pretty much told them you couldn't handle working+studying (which many people do successfully) and also told them you choked.

All true - that's why I am unsure about how to write this - I left the test feeling better than my 160 - I received advice that I did not have to write this addendum but then I saw that I should for two schools I am applying to.

You also don't really have a compelling reason to write an addendum... also, I don't think that adcomms care about an increase of 3 points. You're essentially trying to argue for an extra 1.5 points, and when it comes down to it you're probably not going to get rejected because they look at your score as a 158.5 instead of a 160.