You need to try be patient, and let the inference engine catch up to your mouse movements.
If you pull the dimension away from the edge and it snaps to one of the axis, just move it in a arc until it snaps away and the inference engine should then try the closest alignment to one of the object’s edges.
EDIT: Actually, I do see that the axis snaps seem to be much more powerful, if the origin is one of the dimension line anchors. Ie, the closer to the origin the more powerful the axis snaps.
Also the inference engine will also snap to other dimension’s extension lines, if both dimensions are in the same edit context, But again I experience the same reluctance to align off axis close to the origin.
BTW, a dimension object like most others, can be rotated after creation.
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Preselect the vertical dimension.
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Activate the RotateTool.
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Hover over the bottom vertex of the vertical edge that is being dimensioned.
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Press and drag the cursor up along the blue (Z) axis so you get a Blue rotate around Z axis inference lock. (Release the mouse pick button when the protractor locks to the blue axis.)
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Move the cursor out along the green axis until you get an “On Green Axis” inference, and click. This is the base of the angle of rotation.
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Move the cursor over onto the horizontal edge that you wish the dimension to aligned to, until you get an “On Edge” inference, and then click to complete the rotation.