So the issue is with the setting in your file: webassist/ckeditor/config.js
config.enterMode = CKEDITOR.ENTER_P;
You can see the options for that setting here:
If you use:
config.enterMode = CKEDITOR.ENTER_BR;
Then it will not add an empty P tag, but they don't recommend it since technically all content needs a tag in order to be styled. (you can't add a class or style attribute if you don't have a wrapping tag).
I've also read that you can add the tags:
config.fillEmptyBlocks = false;
config.autoParagraph = false;
config.ignoreEmptyParagraph = true;
Those may also work to address the issue... you would have to play with it to see which one(s) work.
A final option is that you could account for empty P tags on the top of the page in the php code like:
if (isset($_POST["FieldName"]) && $_POST["FieldName"]=="<p></p>") $_POST["FieldName"]="";