Soilcrete for straw bale house

I am building a strawbale house in southern Arizona. It is quite dry and hot most of the year, so moisture is not typically an issues. The plans approved by my local county having Radiant floor heating. This is due to the county requiring that you have heating in every room.
I was originally planning on putting in a earthen floor (3 part native soil, 1. 5-1.25 parts water and 1 part chopped straw) as my base layer. My question or concern is I read here on Permies that someone had issues with the flooring being soft, too soft. Could I solve this problem by doing a Soilcrete (4 inches of native soil, 1/2 inch of concrete, mixed with a rototiller) for my base layer with the radiant tubing inside? My thought process is that the concrete may help stiffen the soil a bit but not too much. Still giving the floor a natural feel, with some back bone.
The base layer that I was intending to do would be 4 inches deep. Then on top of that I would put a finish lay of about 1/2 inch thick earthen flooring. The final lay would have several layers of boiled linseed oil applied.  The alternative is if i do a 4 inch base layer of soilcrete, and put a final layer of 1/2 earthen floor with linseed oil on top.
Oh plus if i did the soilcrete it would save me a lot of time and energy, as of now I would have to dig out my floor sift the soil, mix the soil in the mortar mixer add straw, and water. Then reapply the adobe mix to the floor.
If i went with soilcrete I would have to level the floor add concrete on top. Then take a rototiller and till the soil while adding water to the mixture.
What are you thoughts and Ideas?

Thank you
Bradley

The cement should stiffen the floor somewhat. However, i would not do the till in place method. How were you planning to install the hydronic tubing?  It would be best to have a flat, compacted surface to place the tubing and then place and compact the base layers of 'soilcrete' over the tubing.  I tied the tubing to 6x6 concret reinforcing mesh with thr tubing spaced 9 inches in my house and it works well. The narrower spacing helps because of the lower conductivity of earth compared to concrete.  If you mix the material in place and then try to make little trenches for the tubing, you will end up with inconsistent compaction which will lead to cracks.

Also the hardness of the floor surface is dictated by your 1/2 inch top layer.  The cement added to the base layer won't affect the hardness of the surface.  The sand in the top layer is the biggest factor for hardness.  The mix should have more sand than an earthen plaster.  You could add some lime or cement to the top layer as well.  The important thing is to test a few mixes with your materials before doing the whole floor.