  We push the limit in planning collision-free motions for routing uniform
labeled discs in two dimensions. First, from a theoretical perspective, we show
that the constant-factor time-optimal routing of labeled discs can be achieved
using a polynomial-time algorithm with robot density over $50\%$ in the limit
(i.e., over half of the workspace may be occupied by the discs). Second, from a
more practical standpoint, we provide a high performance algorithm that
computes near-optimal (e.g., $1.x$) solutions under the same density setting.
