I think that Dead Horse may well be closer to the truth than we realise,!!   applying the priciple of Occams Razor, Ie that the simplest and most obvious answer is often the correct one,perhaps to our seafaring antecedents it was so obvious, and they all understood exactly what was implied by the phrase, that they saw no reason to explain it to a bunch of Landlubbers,.
Its only the modern day "Experts" who insist on seeing every little fact written down,recorded , analysed, compartmentalised and backed up by evidence in triplicate !!!!
I suspect if a collecter of such nautical snippetts asked an old salt "Excuse me my good man, that phrase you just sang, exactly what do you mean by it?? "    The reply would have been along the lines of
"Its Fu***** obvious innit Mate !!!!!!"
Anyway its been an interesting thread, I shall now bow out and leave it to you "Experts".