I would seriously doubt that a concrete floor with wide gaps and 1/2" offsets is stable enough to do what you are planning. How can you be sure that the 'continental shifting' won't continue and ruin the new floor in a relatively short time?

JM$.02W

"Does anybody see a problem with this?"

You are not flattening the floor and you cannot "piece" cement board in that manner. Your floor will be nowhere near stable enough for a flooring material. And you have not even addressed why and how the concrete got to the condition it currently is

It sounds like the stability of the floor is the main concern, but replacing the volume of the expensive leveling concrete with something else doesn't have any specific problems associated with it. The room is an addition, probably added 50 years ago, and the concrete shift is slow at this point. I just want to get the floor mostly flat, it doesn't need to be perfect. It's basically a basement added onto the back of the house. It had carpet that got ruined and I want to replace it with something else. It's not a situation where anything is likely to last 50 years. I'm just trying to figure out what I can do that won't cost a ton now, and when the concrete does shift a little more won't be a huge deal. I'm thinking some stick on tiles are probably my best bet. I'll get extras and in 10 years when the floor has shifted another 1/8" I'll have to pull off the ones in the trouble spots, grind the concrete down, and put new tiles on.

Flattening concrete (repair and floating new concrete over top) is EXPENSIVE. It is super expensive. In fact it will cost more than the flooring - guaranteed.

A slab like yours sounds like:

A. It does NOT have a vapour barrier underneath it. If it is 50 years old, it won't have the plastic underneath it = BIG problem with new concrete sticking to old. Getting anything to stick to this is going to be a BIG job...just to stop the water from moving up from the ground to the adhesive.

B. It needs big repairs...if cracks are showing gaps then you need to repair/fill and then add more concrete. That just added a few more days and a few more dollars to this. Not to mention the technical knowledge you will HAVE to pick up...as in you will have to learn the ENTIRE concrete slab business just to do DIY.

C. Your slope is going to be TOO MUCH for anything other sheet products (carpet or vinyl). So long as the concrete is smooth and the cracks are filled you can use SHEET vinyl...Yep. Sheet vinyl. It is fast, and it is tough. And it is water resistant (to people dripping wet....not a flood...nothing survives a flood).

The BIGGEST issue I see is the vapour barrier is missing. This changes EVERYTHING. A glue down tile = lifting in a year. New concrete must be bound to the old. That requires SOOOO MUCH more work than you know. If you had a pro do it, it would cost you $5/sf just to get the slab ready for new concrete. The concrete = $2/sf....but it you do not PREPARE it with water barrier products (grinding and cleaning and filling and water barrier and primer) you are just asking for a whole bunch of crumbling stuff.

I know you want to DIY....but save yourself the effort. Use the sheet product and be done with it. The cost you would spend on the flattening (even the way you are thinking of) will go towards the install costs. At the end of the day it could be in within a few days (cracks still must be filled).

My friend bought a cottage with an old long garage. The concrete floor was cracked and unlevel with no vapor barrier. We spent two days with a rented jackhammer removing the old concrete. About 250sqft. The concrete guys left us their dump truck to load the material. Two loads. It was a lot of work but saved a lot. Vapor barrier and new concrete was easy for the guys. That floor has been dry and stable for over 10 years. For living space you could add insulation board if you're in a cold climate. Hard work for us but over in a short time with lots of future enjoyment.

I finally got around to trying to fix this. I got a laser level so I could figure out exactly what the situation is. The concrete has not risen anywhere but it settled a lot. Just over 2" from the highest to lowest point. I'm filling the low points in with sand topping mix. I do chunks at a time. I've got the lowest 112 square feet leveled. I got the $120 concrete vibrator from Harbor Freight today and it helps a lot with leveling. The 4x8 section I did today looks better and was easier than the sections I did Monday and Wednesday. I'm putting primer down beforehand and using cure and seal afterwards. I figure this is about as cheaply as it can be done. I'm thinking that by the time I'm done with this the floor will be mostly flat, certainly better than it was before. At that point I think some sort of linoleum/vinyl roll will be the best way to make it waterproof. It's possible I'll try some sort of epoxy or other waterproof thing.

Another thing I'm learning is how to work with concrete a little bit. It's something I've wanted to learn for a long time.

How could it be anywhere near the most expensive way? I'll get the room level for < $1,000. I don' t think the slab is sinking anymore. Some of the patch on the worst crack must have been at least 20 years old and it wasn't cracked. It's an above grade slab and this room doesn't seem to have water problems. We've had very wet springs in the last few years and I've seen no water or moisture. I'm caulking the cracks. Worst case scenario is I have to deal with it again sooner than I hope.

we'll see. At this point the most interesting thing about this site is trying to figure out who is giving honest advice and who is being self-serving. Certainly both exist. Nobody is going to take the existing 600 or so square feet of concrete out and replace it for a grand. It's at least 50 years old at this point and quite stable. It seems like adding concrete to fix the old sinking problem is the thing to do but I could certainly be wrong. Time will tell.

Rent a jackhammer or concrete saw and DIY get rid of that. Call a bunch of friends with wheelbarrows and promise them pizza and beer. Call a concrete truck. 2 hours later, screed it off while drinking beer and calling the pizza guy. Cover with plastic. Install almost anything you want in 7 days.