I think your version of saying あらかじめ用意したつゆに sounds better. The writer simply wanted to emphasize the source is for dipping, not just a regular broth. Japanese language uses repetitive modifiers already stated as an adjective.
In other words, you disagree with the wikipedia entry below mentioning the second part of まで, which your answer suggests is unnecessary or wrong?
To indicate ranges (5時〜6時, from 5 o'clock to 6 o'clock; 東京〜大阪 Tokyo to Osaka). In such cases it may be read as ...kara...made (...から...まで)
naruto's points about difficulty are valid; building a romaji converter is much more complicated than a pinyin converter, but it's certainly possible to build a system that does this. I wrote a library called cutlet that does the conversion. You can try out the online demo.
Rendaku occurs when two independent words come together to form a compound. I think 一本気 is a compound, while 本気 and 元気 are not. (Just because they are analyzable as 本+気 and 元+気 doesn't mean they are compounds. 元 and 本 are not independent words, unless you mean "a book" by 本.) Also, Sino-Japanese words don't normally participate in rendaku. In that ...