Create R binary packages for Linux that can be installed on different machines?
Different compiler releases, different libc/libstc++ releases, different "other library" releases, different per-distro release cycles, ... make it that you just cannot match that goal with dynamic linking.
You can get half-way there as e.g. RStudio does by a) bundling all your depends and b) reflecting subsets as they do for Debian/Ubuntu and RH/FC/CentOS. But with a) the tarballs would get massive, as they would with static linking.
In short: you can't on Linux. So back to sources it is.