Zevachim 24a - Dovid or Shlomo: Who gave kedusha to the mikdash?

Rashi writes that the kedusha of the floor of the azara was done by Dovid HaMelech. Tosafos asks that although Shlomo was responsible for building the beis hamikdash, the kedusha was given to it by Dovid in advance of Shlomo's construction.

The Brisker Rav in one of his letters (pg. 81 in Gri"z al harambam) explains that the Rambam holds that Dovid was responsible for choosing the mikdash. The "bechira" of the place was done by Dovid, but the actual sanctity or kedusha was done by Shlomo. The din of "bechira" establishes the makom hamikdash as the only place to construct the beis hamikdash and forbids the sacrificing of korbanos anywhere else. But the actual kedusha of the courtyard and mizbei'ach was done by Shlomo as the Rambam writes in Hilchos Beis Habechira 6:14. The language of Tosafos indicates that they disagree with the Rambam and hold that the actual kedusha was contributed by Dovid, not Shlomo.