Note: This answer is from the OP.
Thanks to DanF, who pointed out that I should look on the website Beurei Hatefila for an answer, and to "go to that site when [I] have a tefilla-orientated question."
First of all, my understanding of the Gemara in question (B'rachot 11b) was incorrect; the preferred wording of the paragraph is not "ahavah rabbah" but rather "ahavat olam"!
ואידך מאי היא אמר רב יהודה אמר שמואל אהבה רבה
Which is the other b'rachah? R. Yehudah said in the name of Shmuel: "ahavah rabbah", an abundant love.
The opinion of Shmuel is that the wording is "ahavah rabbah". The Rabbis, however, say that the proper wording is "ahavat olam", an everlasting love:
ורבנן אמרי אהבת עולם וכן הוא אומר ואהבת עולם אבהתיך על כן משכתיך חסד
The Rabbis say "ahavat olam", an everlasting love, is said, [based on the Yirmiyahu 31:3] "And I loved you with an everlasting love, therefore with affection I have drawn you near."
So the question is not on why the Sephardic custom is to always say "ahavat olam", but rather on the Ashkenazic custom to recite "ahavah rabbah" in the morning (like Shmuel) and "ahavat olam" in the evening (like the Rabbis)!
The following is based on this article from Beurei Hatefila. One should refer to this article.
Tosfot comment that there became a practice to recite both versions to satisfy both opinions in the Gemara, as I had assumed initially. The Rosh wrote that the Geonim said we should follow both opinions, and therefore it is the practice in Germany and France to recite "ahavah rabbah" during Shacharit and "ahavat olam" during Ma'ariv/Arvit.
And interesting reason provided by the Siddur Avodat Yisrael: "ahavah rabbah" is recited during Shacharit and "ahavat olam" is recited during Ma'ariv/Arvit to avoid accidentally reciting the Birkat Kriyat Shema of Shacharit during Ma'ariv/Arvit and vice-versa.