I was dumb enough not to read the entire page. Tae Kim explains it:
"Similar to the difference between 「から」 and 「ので」, 「が」 has a softer tone and is slightly more polite than 「けど」. Though this isn't a rule as such, it is generally common to see 「が」 attached to a 「〜ます」 or 「〜です」 ending and 「けど」 attached to a regular, plain ending. A more formal version of 「けど」 is 「けれど」 and even more formal is 「けれども」, which we may see later when we cover formal expressions. "
Perhaps the question is not so much about opposition between the plain and the polite styles as about selection between desu and masu? Yes, I'd conclude the sentence with ほしくありませんでした. It is, however, increasingly rare, being supplanted by the masu-construction, as the negative past of the masu-form is heavy and irregular (note the position of the negation).