Some more observations. Clearly the usual tune for The Rakish Young Fellow (Tarpaulin Jacket) and the well-known standard tune for ORTB are related. Both are quite simple, though ORTB rather more theatrical and with a greater compass. TJ's tune is usually quite plaintive and slow, more serious, and ORTB much more robust. If RYF did inspire ORTB then the latter might be considered a burlesque of the former. From at least 1838 onwards, as a theatrical piece, various versions of ORTB were extremely popular and constantly parodied into new versions. What for now I'll call the British version was printed almost verbatim by English printers of about the same period, the 1840s, mainly by Successors to the Pitts/Catnach dynasties, but not apparently by Pitts or Catnach themselves. I think it a fair conclusion that ORTB probably did not exist in its standard form during the Pitts-Catnach era up to about 1835.
The language of all versions I've seen is generally, though not wholly, of the theatre of the time, i.e., a certain sophistication, not normally found on street lit or in oral tradition of the period.
e.g., 'That cruel implacable foe'.

The 2 identical versions on the Lester Levy site with no images available start off with the standard British first line but must deviate quite quickly as the subjects ascribed to it on the site do not completely tally with the standard version, although they appear to have the funeral and burial verses in some form.

The Southern Ballad version on Levy which is available has a new first verse but all of the other verses appear somewhere in the 1848 Forget-me-Not Songster version from America reprinted by Louise Pound in American Ballads and Songs.

This American version has a lot in common with the British version but has 3 extra verses and some other verses are shunted around.

What we need to draw any useful conclusions is information prior to 1838, mentions in magazines and newspapers perhaps. The song appears in several musicals in one form or another on both sides of the Atlantic in the 1840s.

On one of the pieces of sheet music the air (the standard one) is described as a 'Tippecanoe' air. Tippecanoe is in Indiana and I'm not sure what they mean by this.