There is a custom of the Gra to replace the regular shir shel yom on holidays and various other special days with a psalm specific to that day. (This custom is followed by many Nusach Ashkenaz synagogues in Israel, particularly in Jerusalem.)

[Here](http://www.daat.ac.il/encyclopedia/images/shirshelyom.pdf) is a list of the relevant days and the psalms recited.

What was the Gra's source for this list?

Some can be found in the gemara (e.g. the various psalms for Chol HaMoed Sukkot are listed in a beraita quoted in [Sukkah 55a](https://www.sefaria.org/Sukkah.55a?lang=bi), and Rosh Hashanah's Psalm 81 is discussed in [Rosh Hashanah 30b](https://www.sefaria.org/Rosh_Hashanah.30b?lang=bi)). Some are found in [Masechet Sofrim chapter 18](http://www.hebrewbooks.org/pdfpager.aspx?req=33833&st=&pgnum=38) (e.g. Psalm 30 for Chanukah).

But some are not found in Masechet Sofrim (e.g. Psalm 32 for Yom Kippur), and some are contradicted by Masechet Sofrim (e.g. Shavuot - Gra says Psalm 19 and Masechet Sofrim says Psalm 29).

So what is the Gra's source for these choices, especially where they contradict Masechet Sofrim?