Should I contact the EIC for additional information regarding his decision on my paper?
I have never been an EIC but I have spoke to some, I have been a reviewer of many papers, and I have had the similar experiences as you described. 

It is probably useless to further inquire about your paper. The EIC decision could have been based on the private communication channels of the review process. The reviewer might have been lukewarm about your paper - maybe it was not a case of a substantial error but that the result was uninteresting. It could also be the case that the new EIC did not have the time for a careful consideration of your paper, of balancing the different reviews and based her decision on the less positive one. EIC are usually very overloaded and some of them explicitly use the rule of deciding based on the most negative review. If it is any of these two cases, you will not receive any further information from the EIC regarding your paper.

My personal experience is that I was only able to change a EIC decision once, when the negative review was reasonably detailed and I could show that some of the  main points made by the reviewer were 100% opposite of what was already written in the paper. The other occasions where I asked for more info or criticized what I thought was a wrong interpretation of the paper, I would receive a polite answer that the decision was made. 

Now, I wait a week until the frustration and the anger of how "dumb is this reviewer" subsides, make the the changes I think are reasonable and send to the another journal.