Even though I am still not a hundred per cent clear, I think that the answer to your question lies in the explanation of the Tosfos ha'Rosh, who adds a few words to those of Tosfos (as he often does). The Tosfos ha'Rosh explains that since, in a number of places, the Pasuk writes "Ulam ha'Bayis", this implies that the Ulam and the Bayis are one (I assume what he means is that they are part of the same entity (according to Rebbi Yehudah). Consequently, when the Pasuk writes "Pesach ha'Bayis", it is as if it had written 'Pesach Ulam ha'Bayis'. The Rabbanan refute Rebbi Yehudah's proof, the Tosfos ha'Rosh explains, because "Ulam ha'Bayis" means (not that they are one and the same, but) 'the Ulam that opens into the Bayis'. As I wrote at the beginning, I am not fully satisfied with the answer, but the Tosfos ha'Rosh does make it easier to understand.

be'Virchas Kol Tuv

Eliezer Chrysler