Visio: Anchor to Sloping Face of Diamond Shape?

In Visio one of the most fundamental and frustrating annoyances I'm facing is not being able to anchor to the sloping face of the diamond shape.

My organization commonly uses this shape in flow diagrams.

Whether it's a densely connected logic point, which needs more than the 5-6 anchors...

...or a self connecting loop like this:

...I often want to connect to the sloping faces of the diamond shape, but can't seem to find a way to successfully anchor to the sloping part of the shape.

Currently I'm settling for connecting one side, but that leads to frustration when things are repositioned.

I've also explored the Data and Format Shape menus presented by right clicking the shape and the path I'm looking to connect to it as those sounded promising. However, examining those menus, I haven't found anything that looks close to what I need yet.

Seems like there must be a way to do this, though.

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Update

I've also tried to redraw the diamond w/ a Pencil in the ribbon's Tools pane under the Shapes dropdown ... but did not have any luck anchoring to the result.

I also have clarified that my question is relating to a basic anchoring need, given my initial example's deviation from traditional UML.

Overview

To anchor to somewhere on a shape face other than the defaults, simply add connector points. (Shift+Ctrl+1, by default)

If this is a common issue, create a master shape with additional connection points to reduce time cost.

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Adding Connectors

In Visio 2010 or later:

1.) Enabling Connection Points

Under Views tab, be sure Connection Points in Visual Aids group is CHECKED:

!! NOTE: If this step is ignored, attempts to add points may fail.

2.) Enter Connection Point Edit Mode

Either enter press Shift + Ctrl + 1 or go to Tools group in Home tab and click the x (Connection Point) to enter appropriate edit mode.

3.) Select Shape

Click to select the shape to be edited.

4.) Add a point

Hold Ctrl and then click again on the desired position along the face of the selected shape to add a point.

(Visio 2013 -- after adding a point)

The point is depicted in Visio 2010 as a magenta 'x', while it's depicted as a red square in Visio 2013. The shape itself is thinly outlined, w/ pre-existing connection points shown as blue 'x's in Visio 2010; for Visio 2013, it's instead depicted as a gray bounding box, w/ pre-existing points show in gray for unselected shapes.

You must select the shape before adding the points, however, once selected as many points as are desired may be added.

BEWARE -- once a shape has been selected, you can add connections on other shapes nearby, as well, leading to potentially weird routing.

Complete!