Density of 1-unstable periodic points for coupled tent maps

Let $f_a\colon\mathbb R\to\mathbb R$ be the skew tent map and let the coupled tent map have coupling parameter $\omega$. Its topological attractor is the closed invariant set containing the metric attractor, the diagonal $\{(x,x)\in[0,1]^2\colon x\in[0,1]\}$. For $a\in(\frac{1}{2}(1+\sqrt{5}),2)$ and $\omega\in(\omega_b(a),\frac{1}{2a})$, the set of $2$-unstable periodic points is known to be dense in the topological attractor, while density of $1$-unstable periodic points there is unknown. Density conjecture. For the coupled tent maps with $a\in(\frac{1}{2}(1+\sqrt{5}),2)$ and $\omega\in(\omega_b(a),\frac{1}{2a})$, the set of $1$-unstable periodic points is dense in the topological attractor. The claim would complete the known coexistence result by extending density from the metric attractor to the topological attractor.