References for these statements:
1/
“The Butchella (Badjala) is a dialect of Gubbi Gubbi”
Australian Languages: Their Nature and Development, Volume 1 By Robert M. W. Dixon (who is the preeminent expert on Australian languages) 2002, in List of Languages and language groups section. The same reference also establishes that these are part of the Greater Maric group.
2/
“which has been extinct for a long time. Indeed, that entire language family is extinct.”
http://glottolog.org/resource/languoid/id/kabi1260
Kabikabi, an extinct Eastern Waka-Kabic language, is missing from E16 ( William Ridley 1873 , Adolf B. Meyer and Max Uhle 1883 , Bell, Jeanie 2003 , Ridley, William 1866 , Holmer, Nils M. 1983 ).
Note that the Wikipedia article infobox also places the language in the Waka-Kabic group
https://en.wikipedia.org/wiki/Gabi-Gabi_language
And that the whole Waka-Kabic family is noted as extinct, again based on Glottolog data.
https://en.wikipedia.org/wiki/Waka%E2%80%93Kabic_languages
3/
“Inexpert notes were taken by James Davis in 1855”
Steele, John Gladstone (2015). Aboriginal Pathways: in Southeast Queensland and the Richmond River. University of Queensland Press. Chapter 12
4/
“and some word lists were compiled in the mid 20th century”
http://glottolog.org/resource/reference/id/6079
https://minerva-access.unimelb.edu.au/handle/11343/36949
“This thesis is a sketch grammar of the Badjala language of Gari (Fraser Island), and is the result of a fresh transcription and analyses of taped material recorded by Professor Stephen Wurm (now deceased), in 1955, 1960 and 1962 with Gaiarbau, the main informant and one of the last speakers of Badjala. These recorded sessions were conducted on Stradbroke Island and Brisbane, before this elderly man passed away in 1964”
5/
“and the spellings have been haphazard.”
This is an observation on my part, made by inspection of the lexicons.
6/
“The use of the spelling “k’g” is atypical for languages of that area”
Again, this is an observation on my part: there are no other words in the lexicons from that language family that start with k’g.
7/
“conceivably Davis was trying to render the fact that the velar plosive in Gubbi Gubbi is unaspirated. In English we aspirate the k sound, so to his ears it probably sounded a bit like a g, a bit like a k.”
The Wikipedia page on English phonology notes that the unvoiced plosives are aspirated:
https://en.wikipedia.org/wiki/English_phonology, in the section on consonants
The phonological notes here suggest a sound between the English g and k for the Gubbi Gubbi language.
https://morayfieldeastss.eq.edu.au/Supportandresources/Formsanddocuments/Documents/Indigenous%20Resources/dictionary-of-the-gubbi-gubbi-and-butchulla-languages.pdf
9/
“English speakers just render it as a g sound. There are no Butchella speakers, and no one who has even heard Butchella spoken by someone with Butchella as a first language, so the English-speaking people who identify as Butchella today also just use the g sound.”
The fact that it is now pronounced as a g-sound is found in several references, including being noted by yourself, but here are a couple:
http://www.abc.net.au/news/2017-04-24/fraser-islands-national-park-renamed-kgari-paradise-aboriginal/8460808
https://www.sbs.com.au/nitv/article/2017/09/26/miranda-otto-kgari-and-correcting-eliza-frasers-remarkably-silly-story