If Big Hero 6 is as big as many people are predicting, I think Giants could continue that trend. Giants and ST3 hopefully wouldn't have too much audience overlap, but I don't think Paramount would be willing to take the risk. I would be surprised if they released ST3 on Nov 23, but I wouldn't quite place it in "impossible" yet.
I don't think June 24 would work, even if TF5 doesn't release then. July 4th weekend will probably be huge, cutting into ST3's legs. The rest of July is pretty big as well with "Untitled Marvel (maybe Dr. Strange), Bourne, Ice Age (which will be huge OS), King Arthur (which may move), and Apes 3.
I'm still going to stick with June 3, just because it seems like the less risky date. However Nov 23, Nov 11 are still (possible) but unlikely. July 22 would be preferable to June 24, but I just can't see it happening. I'll say no to May 20th however, because of the uncertainty of the slate (BvS vs Cap 3, Alice vs X-Men, and Dragon vs Dory)