The edited version isn't wrong, but yours and captain flint's aren't either, and they're easier to read, not delaying the logical connector until halfway through a long sentence.
I think that supposed style rule about not putting 'however' at the beginning of a sentence is a crock. Fowler ed. Burchfield for BE doesn't even mention such a rule, saying only that if it's at the beginning of a sentence it must be followed by a comma. I think they're right.
Garner for AE, however, may be the culprit, as his entry on the topic is distinctly unhelpful.
however. A. Beginning Sentences with. It seems everyone has heard that sentences should not begin with this word—not, that is, when a contrast is intended. But doing so isn't a grammatical error; it's merely a stylistic lapse, the word But ordinarily being much preferable. The reason is that However—three syllables followed by a comma—is a ponderous way of introducing a contrast, and it leads to unemphatic sentences ...
B. Emphasizing Certain Words. Assuming that however isn't put at the front of a sentence, the word has the effect of emphasizing whatever precedes it. ...
C. Undue Delay in the Sentence. Because of the point established in (B), it's quite unwise to put the however very far into a long sentence. The cure is an initial But—e.g.: "We use data only for individuals from the former West Germany in this study, however, and restrict our attention to data reported for the years prior to 1989, the year of reunification."... (Read: But we use data only for individuals from the former West Germany in this study. And we restrict our attention to the years before 1989, the year of reunification.)
I think he's wrong, and his version of that last example is even a Verschlimmbesserung, because it's so unattractive to use 'But' or 'And' at the beginning of a sentence when you're not writing in journalistic style. 'And' and 'But' aren't wrong either, but they should be used relatively sparingly because they create such a sharp, jolting break in the flow of the text. To me 'however' is much less jarring.
But it depends on how many other corrections to the corrections you find you need to make on this paper. If you need to pick your battles and focus on the editor's worst excesses, then this might be one to let go.
What is absolutely wrong, however, is removing the hyphen from 'whole-brain.' Ask the editor to show you the dictionary where 'wholebrain' is listed as a word; I bet there isn't one (but if there is, it's suspect too). That little point I would indeed insist on if possible. Just removing punctuation marks willy-nilly is not editing, it's brain-dead. (Or braindead, as this anti-punctuation person might have it.)
In fact, don't you probably also need a hyphen in 'smaller-volume approaches'? So that it reads [smaller-volume] approaches (= approaches using smaller volumes), as opposed to smaller [volume approaches] (= volume approaches that are smaller)?