While we are on the subject of Rav Soloveitchik's understanding of the Gra and the Baal HaTanya - I though it might be helpful to delve a bit into the related issue of whether Rav Soloveitchik's views are manifestations of the hashkofa of the misnagdim.
I had asked Rav Sternbuch this Shabbos whether he agreed with the Klausenberger Rebbe's description of contemporary chasidus and its leaders as basically as nonthinking/non-intellectual. He responded that it is clear that for most people (not just chassidim) the issues of chassid versus litvak are not understood or even thought about anymore. He agreed that for most people Yiddishkeit is primarily through keeping mitzvos and participating in Jewish life rather than worrying about the nature of tzimtzum or other issues that caused the heated dispute between these two camps. Thus it might be helpful reading about what hashkofa issues were involved in the dispute and whether Rav Soloveitchik seems to accept the idealization of the misnagdim.
Prof. Alan Nadler has raised this question in a thought provoking essay available here.
The philosophical originality of Rabbi Joseph Baer Soloveitchik is widely held to consist primarily in his harmonization of traditional Lithuanian Talmudism with German philosophical idealism. Soloveitchik is heralded for his unusual mastery of these two very different disciplines, particularly for his erudition in culling so richly from them both in formulating his own "modern" Orthodox Jewish philosophy. Personally as well, Soloveitchik is admired as the embodiment of this grand intellectual synthesis, as a kind of model of the "mithnaggedphilosophe."' It is in the first and most celebrated of Soloveitchik's works, the 1944 monograph Ish Ha-halakha (Halakhic Man), more than in any of his other writings, that the composite and synthesizing nature of his religious thinking is most manifest. This work is largely predicated upon the harmonization of the Lithuanian Rabbinic tradition - or the religion of the mithnagdim - with elements of German philosophical idealism. In Halakhic Man, Soloveitchik constructs an ideal religious typology, in a distinctly neo-Kantian epistemological framework, in order to portray his own mithnagdic progenitors, such as Rabbis Hayyim of Brisk, Hayyim of Volozhin and the Gaon Elijah b. Solomon of Vilna.