${SUDO:+...}${SUDO:-...} is not the right ternary — ${SUDO:+x} expands
to 'x' when SUDO is non-empty AND ${SUDO:-y} expands to 'y' when SUDO
is empty, but they're not exclusive substitutions of the same variable
in this context, so 'sudo' (the value of $SUDO when set) leaked into
the output as 'sudosudo'. Replaced with an explicit if/else.