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I have written a peer-reviewed paper for an Australian academic conference. The reviews are favourable with a number of small and helpful suggestions. However, one reviewer has criticised the use of the word "amongst", saying it is archaic and should not therefore be used in a technical paper.

In British English, "amongst" is more commonly used in everyday and technical language, and to my (British) ear, it fits better than the alternative "among" in the context that I have used it. In fact, it was introduced to the language more recently. However, in US English, it is less often used and could be considered archaic. Australian English has many similarities with American English, so it may be considered archaic there too.
My question is whether the paper should be "corrected" to Australian English as it is an Australian conference, or if "correct" UK English should be allowed from a UK writer?

I am not trying to pick a fight, and the acceptance of the paper is not at stake - this is merely a suggestion from the reviewer - but I am interested in what would be considered the correct approach.

My question is whether the paper should be "corrected" to Australian
English as it is an Australian conference, or if "correct" UK English
should be allowed from a UK writer?

British English is acceptable in US-based or other places conferences that do not use British English. Each conference writes their requireements in the Call for Papers. Mostly, international conferences require English. But it is unreasonable to require specific English. Even if it Australian-based conference. Any English is acceptable. Just be consistent in the whole text on the English you choose.

I am not trying to pick a fight, and the acceptance of the paper is not at stake - this is merely a suggestion from the reviewer

I think you (and some of the other answers) are overthinking this. Suggestions from reviewers are precisely that - suggestions. Some are good, some are less good, and you are free to adopt or ignore them at your pleasure. There is nothing at stake here no matter what you decide. Hence, I feel that the analyses of the relative frequency of usage of “among” vs “amongst” in British English, and other such considerations being brought up, are simply beside the point. This is one occasion where you can literally do whatever you want. Feels nice, doesn’t it? ;-)

Until the 70s in Australia we spoke officially in Received Pronunciation and Received Standard was our official grammar standard. Those days are past. And 95% of Australians did not speak that way.

The most official standard is the Australian Government Style Guide. However most organisations do not follow it. Harvard and Chicago are both more popular.

The second most official is the Macquarie Dictionary. See https://www.macquariedictionary.com.au/ (but it's not free).

This is Oxford's Dictionary take on it. https://blog.oxforddictionaries.com/2013/02/05/among-amongst/

The practise in Australia is to simplify older longer words with shorter words. Having said that, not everyone agrees.

Generally, unless there is a specific rule in the call for papers, any geographic variety of English should be acceptable, particularly if it conforms to the formal usage of a country with large numbers of native speakers (i.e., the U.S., the U.K., Canada, Australia, Ireland, New Zealand, South Africa). When there is such a rule, it is most likely to be confined to matters of spelling and punctuation, leaving aside issues of vocabulary and grammar.

The reviewer in this case is likely to be American, as we Americans, forming the overwhelming majority of native speakers and lacking as strong a cultural connection with the U.K. as the other English-speaking countries have, generally have the lowest awareness of usage in other countries. Even if amongst were uncommon in Australia, which it isn't, few Australians would be so unfamiliar with British usage as to comment on it.

It's true that a number of words commonly used in Britain, amongst among them, sound somewhat bookish to American ears. That's because we read them but rarely hear them. "Archaic" is a real exaggeration, though.

I think a tactful reviewer reading a mostly well-written paper with a handful of things that sound odd to them should ideally be aware of the possibility that these might be legitimate geographic variants. Realistically, this won't always be the case.

If it is just the one word amongst, change it and move on. I doubt that the strength or validity of your paper hinges on use of that word.

Now, if they said the paper in its entirety is in the wrong English it would be best to ask the editor whether the journal/conference agrees. It would take a considerable amount of work to rewrite a paper in an unfamiliar dialect, and the strength of the paper could suffer.