Cross Game
That's the best anime romance I think for your tastes. It doesn't fully fit into any of the specific situations you described, but it certainly has that type of flavor.
You might also like
Maison Ikkoku which has a lot more comedy, but also has the flavor of romance it seems you like.
Ranma 1/2 and
Ai Yori Aoshi both fit into the arranged marriage category, but I'm not sure if the flavor of either of those is actually to your taste.
Inuyasha would fit under the reincarnated lovers issue- although I think the Romance is the B-plot.
You might also try
Ah My Goddess, which might fall under the "fated" type.