Can you suggest which common license, if any, could cover this case ?
No, we can't suggest a license for you, because all the conditions you listed in your draft are restrictions that are not allowed in an open-source license.
Else, what should a custom-written license for this particular case specify ?
A custom-written license should be written by a ...
I want to make it so that the modules cannot be hard coded into these engines themselves... The purpose of these being modules is to be switched out and it defeats the purpose of this ability.
In a way, this is exactly what the Lesser GPL (LGPL) v3 requires in 4(d):
d) Do one of the following:
0) Convey the Minimal Corresponding Source under the ...
Don't go this way. Solve the problem like many did before you successfully:
Code and assets are two different things. You should be able to clearly distinguish those. Legally you are not allowed to distribute the assets, unless you have written permission by the original distributors or authors of the original game.
Thus the usual solution is to build your ...
Make those restrictions a technical requirement, not a license one
You don't make that a requirement by putting it in the license. You make it a requirement by not shipping any original or replacement assets, since your replacement engine requires these assets to run the game.
Beyond that, it is pointless to put in any extra copy protection, since the ...