I made a mesh with a decent topology, gave it a subdivision before UVing and UVed it after. Even still, when I subdivide it again after UVing I get some very ugly distortions on my checker textures. How to avoid this sort of issue? Frankly the mesh hardly shifts shape when I smooth, and even still the distortion is disgusting.
A simpler example to see what is happening here:
Now we add a loop cut on the conic part:
And if the loop cuts were on the cylinder part:
In both cases, the proportions are respected in the mesh point of view. But the vertices which are displaced by the subsurface modifier are not at the same position in the UV map. So, they are not kept in place (relatively) the same way.
... a bit hard to explain... but I hope this example is enough to get the point.
In your model, cuts are mainly on the equivalent of the cylinder part here, plus, some are in the cylinder part and others in the conic part (the seam is mixed). So you have distortions.
instead of adding additional loops, you can just go into edit mode, select the boundary between two materials, press shift + E and then press 1 to turn up crease weight for that edge. It'll also cause a sharp edge though, so probably not ideal on a curved surface. In that instance you'd probably need to apply the subdivision modifier and possibly do the uv unwrap again.