You’re trying to use phenomena based, in part, on inertia, in order to form a basis for inertia. It doesn’t work that way.
It’s like the classic problem Feynman described, of trying to describe magnetism in terms of rubber bands… when the elasticity of rubber bands is actually, ultimately, due to electromagnetism.
That leap doesn’t hold. If anything, your argument makes linear motion easier since your suggestion is that gyroscopic stability helps prevent rotation, and thus it’s exactly linear motion that will most readily survive when pushing your hypothetical object.
That’s beside the point, of course, as inertia has nothing to do with all of that. Note that a single atom has inertia even when not connected to anything else, and the inertia of a chunk of stuff is just the sum of the inertia of the individual atoms. There’s no need to find an additional “source” of inertia for the chunk of stuff.