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I think the best way to get a height map to match that is to do it with contours. I have found that the easiest way to do contours is as follows.
Take the map that Waldronate has provided for the land sea as a starting point. Rub out the rivers at this stage so that the starting point is just sea black and land white and no rivers at all. Using this base map, draw black lines on a white background in loops where your high spots are and then keep doing that until you have all of the contours drawn in. Personally I find this easiest with a real pen. A pen tablet is also good but a mouse makes it a chore. Use a scanner or a digital camera to get the real drawing back into the PC.
Then using the contrast tool, whack it up to max so that its just black and white and no shades of gray.
Next, starting with the sea black, use the flood fill tool with black and skip one contour band from the sea and flood the next one in. Do that repeatedly all the way up to the highest contour making a zebra stripes set of contours.
Then you can use the smooth, blur or gaussian blur tool on it a little just to round off any sharp spikes or one pixel holes from the flood fill. Then whack the contrast up to max again and get it to just black and white only. No shades of gray.
Then count how many zebra stripes it takes to get from sea to highest point in the map. Divide your height range by this amount. For most people they would set the sea at RGB 0,0,0 but in your case it could be 94,94,94 so either count (255 - 0) / levels or (255 - 94) / levels. Lets say you had 10 contour bands then it would be (255 - 94) / 10 so use steps of 16 in shades.
Now whist setting the flood fill tool to match with exact color, flood the black sea with 94, the next white one with 94+16 = 110, the next with 126 etc all the way up till you get the highest one at near to 255.
Save a copy of that away for safe keeping. Then use the gaussian blur tool to blur the bands down so that one merges into another a lot. The more contour bands you used the easier this is. So using more contour bands is good.
When thats done you have a height map. Now take the original land sea only mask and multiply that image with the height map and drop the sea to black. Then flood fill it back to 94. This will make the coast line exactly in the shape of the original. Then take the one with the rivers in it and white out the sea leaving only rivers. Ensure that where rivers meet the sea you knock out the sea exactly where the sea was in the land sea mask. Then take the rivers only map and subtract a bit of that from the height map.
Finally, take the rivers map and white out all of the rivers leaving just the lakes only part of that rivers and lakes map and multiply that map with the height map to drop the lakes to black. Then using the flood tool, find the pixel on the height map near to the exit flow of the rivers and grab its RGB color and flood the now black lake with that color. Do that for each lake in turn.
Finally, use a very slight blur just to sort out any aliasing issues and your done.