The up-element conjecture for left-orderable closed 3-manifold groups

Let $M$ be a closed 3-manifold. An almost periodic action of a finitely generated group $G$ on $\mathbb R$ is a faithful action in which the generators act uniformly bilipschitzly, have uniformly bounded displacement, and every point can be moved by at least $1$ in both directions by generators. An element is universally positive, or an up element, if its inverse moves every point a uniformly positive distance to the right. The up-element conjecture. If $\pi_1(M)$ is left-orderable, then it admits a left order associated to a faithful almost periodic action with up elements. This would strengthen the general existence of faithful almost periodic actions for finitely generated left-orderable groups by asserting the presence of up elements for left-orderable fundamental groups of closed 3-manifolds.