I know for certain that the bit about Todai not accepting students over the age of 18 is incorrect. I know 2 people that have become Ronin in an attempt to get into Todai, and they are both over 18.
I'm not too familiar with the foreign exchange program at Todai, but it seems it will be much more difficult to get into Todai, even as an exchange student, compared to another top university such as Waseda. I understand that Waseda has a very prominent foreign student exchange program (that isn't so difficult to get into), and if you are looking to go to Japan to study at a "Top Japanese University", I would consider there as well. Getting accepted as a regular, non-exchange student at either university will be extremely difficult.
Good luck with your endeavor!