You're not likely to find a 'definitive and correct' form; it seems to have circulated orally for a few years before its first appearance on broadsides, as even the earliest differ in content. P W Joyce dated it to the time of the Wexford Insurgency of 1798, which is uncontroversial; though Zimmerman's unqualified use of that date is misleading, as there is no evidence that the song was actually written in that year. Surviving Irish broadside editions such as Haly's are relatively late, and it probably first saw print in London, though presumably it started out in Ireland.

The song has been discussed here a number of times; there are links to older threads in the DT files (ignore the Barbara Dickson one, though; completely different song). The text from Healy (does he not credit any source?) may have been taken from a broadside, as these typically begin 'It was very early'. I suspect that the change in most oral examples to 'early, early' was by analogy with forms of 'Sailor's Life', which tends to open with that line and is often sung to a related tune. Geneva also appears in Carroll Malone (James McBurney)'s 'Croppy Boy'; I wonder if Haly may have borrowed it from that source? Earlier print always has 'Dungannon', I think.

Editions of 'Croppy Boy' at the Bodleian Library