"Yo, heave ho!" -- as a phrase -- has been noted numerous times. I think we've generally seen that it constituted a sort of chant in the pre-"chanties" days. It's still not totally clear to me if it was at all more like a song, if it had more complicated texts, etc. But I have a few more references, to add to the picture.

1807 "A Gentleman Lately Returned from the West Indies." "Descriptions, Remarks, Anecdotes, and Sentiments, during a Voyage from the West Indies to North America, and from thence to England, and during the Author's Rambles in the two latter Countries." _The European Magazine and London Review_ 51 (Feb. 1807). pp110-

It's a voyage in June 1806 from Jamaica to New York.

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About two o'clock P.M. our poor cook died; and soon after, having read the funeral service over him, his body was committed to the deep. An affecting circumstance of him [ cannot forbear here to relate. In the morning he was extremely weak, and some what delirious. The Captain went to see him, and asked him how he was. The poor fellow said he was "Pretty well," and began to sing out " Yo, heave ho!" as if heaving at the capstan or windlass; but soon feeling, as it were, the hand of death already on him, he called out, "Come my boys, heave away bv yourselves, for I can't any longer lend you a hand."
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Dibdin's song, "Tom Tough." This taken from an anthology, _The Universal Songster_ Vol. 3 (London: John Fairburn, 1826).

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...   
    So I seized a capstan bar.
    Like a true honest tar,
And, in spite of sighs and tears, sung out, yo, heave ho!
//

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1854 Unknown. "Down the River." _The Leisure Hour_ 149 (2 Nov. 1854). pp. 698-700.

Musings on the Thames and the Port of London.

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One moment it is the roaring of our captain to some self-willed coal-barge a-head, which has strayed into our track, and threatens us with a sudden stoppage or a collison—then it is the rattling crash of some cataract of Wall's-end into a lighter—then it is the shrill cry of the sailor-boy at the mast-head of some tall ship, or the "yo heave-ho!" of the men at the capstan who are warping her into dock, where she will discharge her cargo...
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1853 Sherer, John, ed. _The Gold-Finder of Australia_.London: Clarke, Beeton, & Co.

Vignettes of the Australian Gold Rush. Preface dated July 1853. Author left England in fall of 1851 on the MARY ANN. Goes to Melbourne. The musical activities of the encamped gold diggers is described. pg. 75

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In my opinion, life in any situation is always apt to degenerate into monotony, unless it is diversified by both physical and mental exertion— at least, so have I ever found it; and even the diggings, with all their excitement, would have engendered ennui, had other resources than gold-seeking not opened themselves, of a more ideal or intellectual character. These were found in the music, the dancing, and the literature of the diggers, all of which were of such a mixed and various kind that their quality might readily be mercifully dealt with, in consideration of the variety which they offered to the gratification of the senses. The musical instruments consisted chiefly of accordions and flutes; here and there a stray fiddle might be heard within the precincts of some Irish tent, or a cornet-a-piston blowing mellowly from the lips of some German, who sent its notes swelling over the ranges or amongst the woods with a sweep that transported the ear far beyond the sounds of the cradle or the pick. A German hymn, sung in chorus, would occasionally relieve this, which again would be lost in the ruder throats of a party of our own Anglo-Saxon seamen, who, with "Yo, heave ho !'' or some such capstan or windlass chorus, would rend the air as one would think they were endeavouring to do their lungs from the stentorian force with which, every now and then, they would commence the first note of the burden of their song. All this was, more or less, to be heard nightly; but it was on Saturday evening, when the end of the week had brought to a close the toils of the labourer, that enjoyment was more particularly on the wing...
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http://books.google.com/books?id=F80NAAAAQAAJ&pg=PA75&dq=%22yo,+heave,+ho%22+cap