Is this for a writing position?
We know that you feel the way you're talking about because you're the one saying it. So we can eliminate three words at the beginning of the sentence.
My experience working on press releases, media kits, speaking points, and media contacts for the March of Dimes, as well as my agency work and familiarity with client contact at Jay Advertising make me an excellent candidate for this position.
Notice that I changed "makes" to "make." Your experience and your agency work and your client contact make. I'm assuming that you did all the press releases and such for the March of Dimes. If not, then I have muddled the meaning of your sentence and I apologize. But that's how it looks from the original.
Now, I am also assuming that you told your interviewer that your work at Jay advertising as with an agency during your interview. So there is no need to rehash that it's agency work. If you want to include everything you had in the original sentence, then you really should separate it into at least two sentences.