To clean up the congested view of the material use the show map icon and instead of showing All ID' S, select the ID 3 corresponding with the orange checker that we want to view.
All that remains is the UV assigned faces having the ID 3.
Now in sub-object mode select "Select Face".
Go into the option Edit UVW while clicking on the Unwrap icon Options. To activate Constant Update and Show Selected Vertices.
Select the common points on the right, and in the viewport the corresponding vertices are also selected.
Although projection is in 3 dimensions, we work in 2d on a UV plane.
The goal being to obtain one UV plane unfolded without distorting the checker.
Rather than working with the object in 3d, with the tools of traditional modeling, we move the mapping coordinates onto a 2d plane, which is simpler and faster.
We will be move the points Horizontally until the checker texture is no longer stretched.
What we have just done is equivalent to a mapping these 3 polygons only.
Here that goes quickly because it takes less operations to select it then it would to map etc. Because we only move the points in 2d space.
We will make the same adjustments for the other points by watching the result in the viewport.
Drag select the next set of Horizontal points and move them cleaningup the texture as we go.
Continue for each column. At some stage you will need to select the points from the other side.
Even them all out to match the dimensions.
Here we arrive at a delicate part of the object because it is not good enough to just move the points, it will be necessary to detach the UVs as we would detach the faces of an object then apply the mapping.
You may get a different set of faces than the ones shown by the pictures to the right but the process is the same.
Select any faces that don't conform, as shown opposite in User View (always in UVW Unwrap: Select Face mode).
Click on Planar Map, and select the faces to receive mapping according to the average of the normals.
Make the same selection for each of the two faces at the ends, and one after the other apply a UV Map.
Open Edit UV and select the ID 3.
We can see that the successive mappings are superimposed.
To put them in order, select a point of the main piece of UV (a set) and by clicking several times on the Expand Selection icon, extend the selection automatically with all the UVs.
Finally move the selection.
The 3 other sets of UV that come from the mapping are superimposed. The gray square which appears in the center of the Edit UV screen represents the mapping of the Gizmo.
The three maps preceding the Gizmo are dimensioned with the exact size of the selected faces.
To separate them click once on a point and use the Expand Selection icon to recover the complete set.
Move the set and repeat this operation as above to have the 3 pieces of UV.
Depending on the faces you needed to manipulate you may need to do this next step.
Move the vertices east to Redimentionalize the squares then weld them to the like vertices with the Weld Selected icon.
Check that you weld the points between them in the viewport of the corresponding points.
We can regulate the tolerance in Unwrap Options.
Use Scale non-uniform if required for the horizontal or vertical lines.
Keep adjusting the UVs according to the viewport until you have the pattern matching.