Richard, When I read your last statement, It appeared to me that you were stating that you want the shadows to behave exactly as they do now. You have an object with a shadow offset 'down and to the right'. After rotation, the shadow remains 'down and to the right'.
When the objects are rotated 180 degress, the shadow does remain 'down and to the right'. This shows the shadow is not rotating with the object. It remains in position relative to the 'global light' position defined by the X & Y offset set in the Drop Shadow dialog, which remains static in relation to the page.
Since we cannot rotate the actual page (all rotation is object level), you will always have the problem of the shadows apparently reversing direction relative to the objects when rotated unless the shadow feature is revamped to allow linking to the object's rotation.
There are situations where a 'global light' may be preferred to a 'local light' for the shadows. It is also true that I have found reason to desire a 'local light' or a shadow linked to the object orientation, rather than the page, for reasons very similar to the table tent example. However, it is relatively easy to simulate that function by applying the negative value when the objects are rotated 180 degrees.
There is no doubt that the shadow effects within Photoshop are more robust and mature than those of InDesign. We can hope that IDCS3 (ID5) will have improvements in this area. I would prefer a dialogue with similar features: an offset distance value, a radial selector for direction (with a text field for manual entry), etc. The X & Y offset is not as intuitive to me.
-mt