1. Use the DisplayDepth effect to first display the depth map, and then edit it to fit the scene. It seems mostly a scale issue, but possibly also offset (position). Note the values you have to put in in order to get the correct depth map which aligns with the your image from the game.
2. Then, click on "Edit global preprocessor definitions" at the top of the lower half, above the options. There you have to create one or several new strings with their respective values. DisplayDepth tells you exactly how these strings are called (see screenshot). Note though that you don't write the "=" which only appears in the .ini file itself, here you just create the string and add the value into the adjacent field. If you typed something wrong (as I first did), you'll get an error message from ReShade that a load of effects couldn't compile. In that case, just go back to the "Edit global preprocessor definitions" section and remove the added string.
What you're basically doing is you use DisplayDepth as a way to display the depth map (depth buffer) to sort out what's going on, and in the second step you tell ReShade to change the depth map accordingly. Since it is a GLOBAL preprocessor definition, it means now you have fixed problems with all other depth-based effects as well as all effects now can use the fixed depth map (any ambient occlusion effect, depth-of-field, distance fog etc. etc.).
Great video you made by the way, it helped a lot in identifying the problem.