Dear Dan,
thanks a lot for this hint. The idea is great:
1) Negative Buffering with the half of the diagonal of my rectangle.
2) Spatial Join with input polygons and output polygons.
But: It didn't work with the value of half of the diagonal of my rectangle although there obviously would be any more space inside of the input polygons - at least in some of them.
By trying with increasing negative buffering distances I found out that it worked until -370 m (I would need -992 m). I got a message that some of the features have been skipped "because a negative or very small distance resulted in no geometry". That wouldn't be a problem as long as I can push it to the limit. But still there are considerable output polygons in 20 of the input polygons but I can't buffer with bigger distance values.
Why? Is there any reason or idea about how to outsmart ArcMap?
Thanks,
Matthias