This question might be a candidate for English Language and Usage, but one term I think you're leaving out is "Acoustician." From the title alone, it seems like you're looking for that, but acousticians really don't concern themselves with electronics as much as they do with the physics of sound.
For your purposes, Producer is probably the broadest term possible with the best connotations. Professional record producers do all sorts of jobs at different levels, from playing background instruments on a record, to composing the instrumental tracks for singers. Highly paid professional producers hire other people to do their engineering for them, but they've got to do it themselves when they're just starting out. I think all of the terms you listed could be jobs that a producer could do at one point in his career.
However, rather than picking the term that sounds the most impressive, I'd use the term that most accurately describes what your specialty is, or what you would like to do. I'll speak from personal experience when I say the notion of a single human being becoming skilled to the level of expert in all of these fields is incredulous to say the least, and would be legendary at best. In most cases, it's just not practical, especially when you consider all of the marketing that a producer has to do on the business side of things to boot.
For example, many people that fill a lot of these qualities (not to mention composing, teaching, etc.) dedicate their lives to making music and performing, so they call themselves musicians. Self-driven musicians will have to do a lot of the production work you mention on their own, especially if they're not signed to a record label! And although they may have a line on the back of their album identifying themselves as the producer, they'll still introduce themselves as a musician, since that's what they would like to be recognized for.
