Hashem’s Bracha to Avraham

At the beginning of Lech Lecha, Hashem blesses Avraham with multiple expressions of blessing. One Rashi connects the blessing of his name becoming great to adding a heh onto his name, changing its gematria from 243 (of Avram) to 248 (of Avraham), the total number of limbs in the human body. Another Rashi connects these brachos to the fact that we’ll mention “the God of Avraham, the God of Yitzchak, and the God of Yaakov” in the first bracha of Shmona Esrei. What’s the meaning and significance of these tenuous connections?