Eero,
I'm not an OS X developer. However, to me, it appears that SDL (and most games) use a full screen mode that's incompatible with the standard OS X alerts and dialogs. That's my guess why most games have their own alerts that are totally different in look than the system. I'm betting that SDL isn't creating a window in the traditional OS X sense. I don't know if SDL 2.0 is any different in this respect.
I think either of your alternative solutions would work fine. However, I have no idea how much work it would be for Jerome to implement any of them. I would love to learn OS X development but, for my job, I would need to learn .Net first.
Bob C