Joseph Dindinger (not aware of ANY Sinaiticus controversy) pointed out that the red ink surely did not look ancient (and the ms. as a whole as well.)

"it did NOT look to be 1600 years old"

It also has annotations in red ink, which is my understanding fades a lot sooner than black ink. So it just looked to me like it was a lot newer than the middle of the 4th century.
So on this thread we will place lots of information about the rubrication of Sinaiticus, where Song of Songs and Psalms are leaders of the pack.

The project (Facebook and PureBibleForum) began yesterday here:

"it did NOT look to be 1600 years old"
rubrication anticipation

And related.

Song of Songs - speakers identified in the text

healthy skepticism of 1860s scholars about Song of Solomon - and the complete NT - "not a word is wanting"