How can minimize edge crossings in using cytoscape dagre? - cytoscape.js

Question

In the following graph:
it's obvious that by swapping l3_b and l3_c the graph all edge crossing will be removed.
The graph is fairly simple. But the dagre layout seems to "miss" the possibility of reordering those two nodes. It was my understanding that dagre will try some heuristics for minimizing the crossings between layers, at least they mention Jünger and Mutzel, "2-Layer Straightline Crossing Minimization", in dagre's recommended readings.
I understand that there is no guarantee that it will find the optimal ordering in the general case, but is there any way to "force" cytoscape's dagre to "try harder" for simple graphs like this? Or is there any other similar layout algorithm that will provide more optimal solutions (even at the expense of slower computation)?
Here is the code I've been using:
import cytoscape from 'cytoscape';
import dagre from 'cytoscape-dagre';
cytoscape.use( dagre );
var cy = window.cy = cytoscape({
container: document.getElementById('cy'),
elements: [
{data: { id: 'l1'}},
{data: { id: 'l1_a', parent: 'l1'}},
{data: { id: 'l2'}},
{data: { id: 'l2_a', parent: 'l2'}},
{data: { id: 'l2_b', parent: 'l2'}},
{data: { id: 'l3'}},
{data: { id: 'l3_a', parent: 'l3'}},
{data: { id: 'l3_b', parent: 'l3'}},
{data: { id: 'l3_c', parent: 'l3'}},
{data: { id: 'l3_d', parent: 'l3'}},
{data: { id: 'link_1', source: 'l1_a', target: 'l2_a'}},
{data: { id: 'link_2', source: 'l1_a', target: 'l2_b'}},
{data: { source: 'l1_a', target: 'l3_a'}},
{data: { source: 'l2_a', target: 'l3_b'}},
{data: { source: 'l2_a', target: 'l3_d'}},
{data: { source: 'l2_b', target: 'l3_c'}},
{data: { source: 'l2_b', target: 'l3_b'}},
],
style: [
{
selector: ':childless',
style: {
'label': 'data(id)'
}
},
{
selector: 'edge',
style: {
'width': 1,
'line-color': '#ccc',
'target-arrow-color': '#ccc',
'target-arrow-shape': 'triangle',
'curve-style': 'bezier'
}
}
],
layout: {
name: 'dagre',
rankDir: 'LR'
}
});