OmniGraffle: How to make line terminators connect to Center of objects, not to the edges of the objects?

You can use the magnet editor to create a magnet wherever you want on the object. Luckily, the center of objects is a natural "snap to" location for the magnet.

Once you have a magnet set in the center, you can easily terminate your lines at that magnet.

Tedious, yes. But, possible.