Strawbale construction will meet your requirements for sound insulation and fire resistance, especially with a clay or lime plaster. I looked up some basics on building code in your county, and unfortunately, it looks like your going to have to get this one permitted, unless your willing to drop the square footage to 120 sq.ft. and skirt it by considering your project an accessory structure like a shed. The bad news on that is you will have to pay building inspectors which might add to the cost and make it more difficult to do everything you want with the budget you laid out, but not impossible depending how you source material. The good news is there was new IRC building code written back in October which makes working with and permitting bales a lot more friendly. A good start would be to read through Bill and Athena Stein's book 'the straw bale house'. Its a classic, but will tell you most of the things you will need to start your build. The new IRC ammendment for bale construction can be found numerous places... this link was the first one that came up on my google search. http://www.strawbale.com/irc-code-2013/
Scroll down to find the link to the .pdf Good luck, keep us posted.