How to apply displacement modifier on globe with mask?

Question

So I have a globe, made with this texture that I am using as a mask.

I wish for the land to be extruded outwards slightly a la this exactly like this question (see below), with the oceans either completely transparent or excised. Wireframe too (but I can probably do that on my own).

How do I go about doing this? Maybe I am missing something, but mine looked like a very spikey sphere when I tried to do a displacement modifier. I tried several tutorials/SO questions, and I am embarassingly more confused than when I first started.

Thanks for any help you can provide!

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Update #1

Right, so progress has been made! I tried susu's suggestion (again) and unlike the first time it worked!

One last thing:

1. How do I increase the "height" of the displacement? I.e. extrude "outwards" or normal to globe's origin.

   • E.g. like in the first image above (see how NE Brazil/Eastern Spain has what appears to be a ~50km vertical cliff, as it would appear to a person).

2. Given the level of detail, I would imagine that the edges need to be smoothed, possibly significantly crisp? If so, how does one do that?

   • So complex topography, e.g. the Chesapeake Bay/coast of Norway would not look like a ball of rubber bands/M.C. Escher having a stroke.

Without "ocean" visible

With "ocean" visible

Materials

Outliner (might be helpful to experts/hapless noobs stumbling across this in the future):

 - Scene
   - Camera
     - displacement globe
       - displace sphere
         - globe displacement material
       - Modifiers
         - Subdivision

     - solid globe
       - solid color sphere
         - globe solid material
       - Modifiers
         - Subdivision

     - Sun

     - wireframe globe
       - Sphere
         - globe wireframe material
       - Modifiers
         - Subdivision
         - Wireframe

(as you can see, 3 spheres inside each other, with displacement sphere extending outwards.

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First Attempt

globe

materials