So Cal garage conversion: Proper way to level floor

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I own a tract house built in southern california built in 1995. There was a builder option to have a 3 car garage (standard 2 car with tandem garage) or a super family room where the extension creating the tandem garage is used as part of the family room instead of garage. My house currently has the 3 car garage and I would like to convert it to the super family room. I pulled the original building plans (which are terrible quality) but I can tell that the current wall separating the tandem garage from the house is not load bearing. I feel like this should be a fairly straight forward conversion but after talking to drafting professionals and contractors they seem to make it out to be a much larger job and have left me with a couple specific questions:

The current garage floor slopes from back to front (as expected) 1 3/4 inches to 4 inches. I am wondering what the proper way to level this flooring is so I can conform with building codes?

Does this require a structural engineer (as has been suggested by a couple drafting professionals)? I thought it would just require additional concrete with some bonding agent…

(Updated 5/18/18) I had one architect+engineer tell me that the city is going to require the slab be replaced because it was not constructed with a moisture/vapor barrier under it. Does this sound right to anyone?

Another suggestion made by someone who used to be in construction was to use 2×4's on their side to frame out a floor and shim up to level. Thought I would throw that out there as a possible suggestion and see what people think.

Here are some images so you can get a better idea of the space and slope:
Rear of garage

Living space foundation height

Garage overview

Best Answer

I would check Cali codes, but here in WA you can do all of those things you asked about without a permit. It would be considered a remodel and only certain things like some electrical work would require a permit. I personally would frame in the garage door area and use the self leveling product you can buy from the local home improvement store that mixes with water. Works well on concrete. I have used it to level and seal over my old basement floor that consisted of thin asbestos tiles over concrete. Have you talked to a local contractor? Ask friends/family for a trusted remodel contractor that will give you an honest assessment would be advice before doing anything.