Straw and adobe usually go hand in hand. Do remember you are not talking about 4" framed walls with this method? If you are trying to adapt to existing slab foundation and plumbing, nothing may match up? You have to think in terms of straw bail width for all your infrastructure systems. You have nothing to nail electrical boxes too or anchor pipe. You may be forced to run everything surface which could be cool looking. I honestly do not know but rather than sneaking around and thinking you can get away with this? Why not talk with a designer or architect who has been down the path?
I would not assume you could not build this way but suspect you will not get away with it in LaLa Land. Straw and adobe construction is wonderful energy wise but it is not exactly a cheap method of construction to meet code. You did not say specifically, but I am assuming you are planning to stay in Southern California? A friend had a beautiful straw and adobe home in Santa Fe that an architect plunked perfectly on the small lot. I had my home in N California at the time and spent, in winter months, what he did for an entire year in heating and cooling.
Sorry to hear arsons took the house but I guess it works out alright for you if the building department says you are good to go. There is not a floor safe with coke and billions in pesos or a few million euros you need to resolve is there? I kid you not, friends closed and moved into a house in Cupertino only to find themselves surrounded by a swat team. They did not even know the home had the safe found (and they never asked what was in it). As soon as they flipped on the lights it was assumed somebody had come back. Police and DEA never checked to see the place had changed title. Funny story after the fact I guess.
Have you thought at all about prefab? I don't mean tacky stuff, I mean highend, factory assembled from a real architect's drawings house. A friend does them in Holland and they are so nicely constructed. No cheaper because his clients put whatever money they saved in a sticks and stones framed from piles dumped in the driveway approach to construction into enhanced finished work. Seems like your labor force would be as willing to help you finish a house as build it from scratch?
Go to the library or look online for possibilities. I remember a book called something like "Prefab Mansions" which is not your goal I know but it will help shatter the stigma and image that comes to your mind when I mentioned prefab and you were thinking trailer park? Sears sold houses once believe it or not and most in Illinois are historically registered. They were not exactly modular in the sense I am suggesting but were kits.
Google, DuckDuckGo or Bing search for books with the main title "Prefabulous". I think there are several in sort of a series by the same authors?
If you consider prefab you will need to find a builder, building designer or architect familiar with the technology. NO! They are not just for the rich and in fact architects have always saved me oodles on projects. All of mine even know how to hold or swing a hammer.
Believe it or not though, one of the obstacles to more prefab housing in this country is proximity of factories that can produce the modules to the construction sites. Only so many are allowed on highways in a given timeframe given they block lanes of traffic and weigh more than a few pounds. Can you imagine what people will be saying behind the wheel as your home moves near you on 101?
Now then let me bridle my enthusiasm. I doubt you are going to pull off even a small 1300sf home near anywhere in S California for $100K so be realistic about that. Won't permits, bribes and building inspectors cost you at least half that? Have you checked to be sure you can build on the foundation you have? It is still to code or can be grandfathered, etc.
Good luck. Could work out great. Do keep posting your progress? I walked away from a dream home project for myself once. I have lived in nice places but go for it when you can! I do like your approach of rescuing something from the ashes!