Roots of polynomials with bounded integer coefficients

It seems that the following paper (linked by Baez on the webpage you link above)

https://www.e-periodica.ch/digbib/view?pid=ens-001:1993:39::181#568

of Odlyzko and Poonen implies that there is an interval in which $R_1$ is dense. Namely, there is some $\delta>0$ so that the interval $[-\phi^{-1}-\delta,-\phi^{-1}]$, where $$\phi=\frac{1+\sqrt{5}}{2}$$ is the golden ratio, is contained in the closure of $R_1$. See the bottom of page 318 to page 319 (see also page 330 for specific values of $\delta$ that work, and page 325 for remarks on results specific to $R_1$). In fact, the density is achieved already by numbers which are roots of polynomials with coefficients all $0$ or $1$ (no $-1$'s necessary).