OK I figured it out. It IS the images.
I reproduced it all in max with various settings BUT I will not bother converting or uploading the results as well
Stick the heigh map into gimp ps or any editing tool RAMP up the contrast. You will then see these SQUARES in the images themselves. It isnt apparent at first but they are in the images. I suspect the tool being used to generate these is using some sort of algorythem based on some sort of square math IE breaking elements down into sections
Attached is a zoomed in and contrast adjusted image zoom is X2 These artifacts exists in both files BTW.
image showing these block artifacts Not use if this is jpg because jpg DOES work on that decimating square regions to compress the images. (never use jpg EXP for grayscale as it is always larger than a lossless PNG and horribly inferior)
NOW because this map is so dim IE it only contains 69 levels after it has gone through jpg vomiting. Likely half that prior to being JPGed. You only have that many LEVELS of adjustment. SO if you took this image adjusted it to have a absolute white and absolute black and you will see it stairstep all over. SO I suggest outputting a huge version of the images,smoothing then unsharp masking the diffuse map then resampling down and running unsharp mask again and using that as displacement BEST is to see if the tool can output a proper displacement map containing all 4 shades as this will give you even more to work with.
Attached is a rendered image using a filtered and processed version of your diffuse map. Yes it dows show some rez issues as I am too close for the rez of the maps used. To smooth it I used edge preserving smooth in PSP7 then unsharp mask. Latter you have to be careful of not to create pillow hotspots or haloing so you'll have to fiddle with it. (Just do not use "sharpen")
FIXED diffuse map
Render with DIFFUSE maps used in displacement slot only. INCREASED the strength to amplify any possible artifacts. It is a bit mushy as I am zoomed into the object and really just too close for the overall size of the map.
just use the strength setting in the displacement map to control how much it displaces. If this is missing I am sure some sort of blend or mix material to dim the map would be better than a crushed spectrum image.