The op's pics show a cable run with multiple S-shaped bends.
A moment's thought should make it apparent to any cyclist that the cable inner when taut will "cut the corners" of an S-bend and that's what causes the "stretchy" feeling. This will happen even with compressionless housing, as what happens is the inner just increasingly takes up the clearance between it and the outer. On single curves it takes it all up at once, then no stretchy feeling after.
Unfortunately the op's choice of bars/stem/levers/wrap and the internal-routing make it difficult to avoid such bends.
Internal routing, like seatpost flutes, is almost always a bad idea.