This is PMC Europe theater:

I did my own elevation map, because of I am not able to export detailed elevation map of theater from DEM2terrain. I can set the colours for different highs very good inside DEM2terrain. But exported bmp doesnt respect my colours setting and it looks still the same - like on the picture above...
So I did another map, using 3DEM software.
But my new bitmap doesnt fit the theater of course. It has an other georeference system.
I have set cornes of the area(we know lat/lon), and then cropped the image:

Can be I am making misstake already in this step, but I hope
data projection is still the same(cilindric), doesnt matter if I load them to DEMtoterrain or to 3DEM.
So I think the most preblematic is next step. Change this above shape ("trapezoid"?) to square (our theater).
I did it two times.
1) Deformation in bitmapeditor:

2)I mapped image onto polygon in 3D program, them stretched and rendered. Result here:

In both cases the cornes are good, but everything else is totally wrong

In conclusion:
a)what projection does use the data stored in this page:
http://www.ngdc.noaa.gov/ (from terrain tutorial)
b)Which transformation does DEMtoterrain software during mysterious "spherical conversion" - simple stretching doesnt work
Thank you
Luk
P.S.
I know, Arc gis software and similar can handle bitmaps much more clever using some reference points, but is there some simple way?