Imperative signatures

When I was little, I somehow learned to interpret the word "love" in letter signatures of the form "Love, X" as imperatives. As in, "I demand that you love me." So recently, when I signed a father's day card, "Love, your oldest son," I mentally added, "but love your youngest son too." Of course, this must be wrong. What most letter-signers mean by the penultimate "love" is probably something synonymous with "with love". It's a sort of sentence adverbial modifying the signature (or indicating something about the signer's sentiments about the signature or the whole letter) like "sincerely". I seem to have developed this misinterpretation on my own as a child. Certainly no one said, "...and the word you write before your name is interpreted as a command." So now I wonder, are there others out there (mis)interpreting signatures in the same way? Is this like some sort of speech act eggcorn that could gather steam in the language?