Snapping one mesh to another while rotating I'm using Blender 2.91.

I've snapped the Mesh A onto Mesh B at point 1. I've made the pivot point of Mesh A to be at 1.
I'd like to be able to rotate Mesh A on the X axis and have it snap to Mesh C at 2. I can get it super close by hitting (R)otate, then X, then holding the shift key while mousing, but I would rather it snap precisely onto its target.
Am I missing any setting for this? The &quot;magnet&quot; feature doesn't seem to work.
After I've gotten it super close, I know I could do an Edit Mode vertex snap (the two vertices of the right side bottom end) to Mesh C at 2, then do another (left side bottom end of Mesh A) to snap to Mesh D. But, this will change the width of the Mesh A. Super close, but not precise.
Someone on my last question (that was also about working with precise, angled objects) mentioned Blender not being a purpose-built CAD software. I can understand that, but it seems like this feature would be one that would come up whenever working with precise dimension objects at non-XYZ angles. I'm not terribly upset about the feature not existing, I just want to try to make sure I'm not missing something.
If you want, you can set a structure up to do this, although I think most people would consider it a workaround:
Create an empty at 1 (&quot;e1&quot;) and an empty at 2 (&quot;e2&quot;).  Give e1 a damped track constraint targeting e2.  Parent A to e1 with keep transform.  Turn on snapping and transform e2 (either rotating about a pivot point or just translating.)  As desired, unparent A with keep transform.