Some say that R' Yehuda held that there is no Biblical source for the 20 amos limit and therefore ruled that a succah could be higher than 20 amos. But that would seem to go against the Gemara that says סוכה דאורייתא תני פסולה מבוי דרבנן תני תקנתא. And if he held there is no source, why did R' Yehuda rule that a מבוי which is דרבנן does not need to be lowered. This suggests that he did have a Biblical source for allowing a higher than 20 amos succah.
I think you are misunderstanding the line of דאורייתא תני פסולה מבוי דרבנן תני תקנתא.
Here is the passage in context:
תנן התם מבוי שהוא גבוה מעשרים אמה ימעט רבי יהודה אומר אינו צריך מאי שנא גבי סוכה דתני פסולה ומאי שנא גבי מבוי דתני תקנתא סוכה דאורייתא תני פסולה מבוי דרבנן תני תקנתא ואיבעית אימא בדאורייתא נמי תני תקנתא מיהו סוכה (דנפישי מילתה) פסיק ותני פסולה מבוי דלא נפיש מיליה תני תקנתא
We have learnt elsewhere : If the [cross-beam above an] alley-entry is more than twenty cubits high, it must be lowered. R. Judah says this is unnecessary. Now wherein lies the difference [between the two cases that] with regard to the Sukkah it is declared NOT VALID, while with regard to [the cross-beam over] the alley-entry, a remedy is indicated? — With regard to the Sukkah, since it is a Pentateuchal ordinance, it [was proper categorically to] state, NOT VALID; with regard to [the cross-beam over] an alley-entry, however, since the injunction is only Rabbinical, a remedy is given. And, if you wish, you may say that even with a Pentateuchal command a remedy may be given, but with regard to the Sukkah, as the ordinances relating thereto are many it was briefly stated, NOT VALID [while in the case of a cross-beam over] an alley-entry, since the regulations thereof are not many, a remedy is indicated.(Soncino translation)
It does not mean that the Torah says that a succah cannot exceed 20 amos in height, as that would, of course, refute the opinion of R. Yehuda. What it means is that the Sages used the term "invalid" because (according to their view) the invalidity of such a succah is already established by the Torah, so they can refer to such a succah as invalid. As opposed to a mavuy where the cross-beam is not discussed in the Torah, so saying that it is invalid if higher than 20 amos is meaningless because prior to the Mishnah there is nothing that makes it invalid. Thus, the Sages instead say that it must be lowered.
R. Yehuda disagrees in both cases. He does not agree that the Torah stipulates that a succah must not exceed 20 amos. Once the Sages declared it invalid, R. Yehuda responds that it is valid. By the mavuy, once the Sages said that it must be lowered, R. Yehuda says that it need not be lowered.
This is essentially Rashi's explanation:
סוכה מדאורייתא. דעשרים אמה דילה ילפינן מדאורייתא וקודם שנשנית המשנה נאמרה שיעורה מסיני: תני פסולה. שייך למיתני בה לשון פסול כלומר לא נעשית כתורה וכהלכה: מבוי. דכוליה מדרבנן דמדאורייתא סגי ליה בשלש מחיצות ואינו צריך לקורה זו אלא מדרבנן: תני תקנתא. דלא שייך למתני בה לשון פסול דמאן פסלה קודם שנשנית משנה זו הרי היא תחלת הוראתו ומצותו
R. Yehuda's source for his view (as explained by Rambam in his commentary to the Mishnah) is that he disagrees with the premise that a succah is meant to be a "temporary dwelling".
Additionally, regarding the basis of R. Yehuda's position, Rashi states that the disagreement will be explained in the Gemara. The Penei Yehoshua points out though that the Gemara never explains R. Yehuda's position. He first suggests that when the Gemara offers three explanations of the Sages' position, and asks a question on each one, we simply assume that R. Yehuda agrees with the questions. However, he then argues that for the first explanation that can't be true (based on a later Gemara), so he then suggests that Rashi was only referring to the reason according to the explanation of Rava which is the explanation accepted l'halacha. As that explanation is that a succah must be a "temporary dwelling", it is understood that R. Yehuda does not require a temporary dwelling.
R' Yehuda holds that a succah had to be both Temporary and Fixed from the verse: בסוכות תשבו שבעת ימים אמרה תורה כל שבעת הימים. Temporary from the word "שבעת" as you see from Rava's explanation and his rationale of why a perfect succah above 20 amos is פסולה. It has nothing to do with the materials used, as the Gemara states: למעלה מכ' אמה דאדם עושה דירתו דירת קבע כי עביד ליה דירת עראי נמי לא נפיק but instead the space in which it is built. And he holds Fixed from the word "תשבו" as you see from Daf 28b כל שבעת הימים אדם עושה סוכתו קבע וביתו עראי. As the Gemara states: "מה"מ דת"ר "תשבו.
Hence the Mishna states Daf 28b: כל שבעת הימים אדם עושה סוכתו קבע וביתו עראי
Therefore, the Rabbis who disputed R' Yehuda taught in a Barasisa: כיצד היו לו כלים נאים מעלן לסוכה מצעות נאות מעלן לסוכה אוכל ושותה ומטייל בסוכה
And R' Yehuda taught: עושה סוכתו קבע וביתו עראי means to build a succah in the 3-denominational space where a house would be temporary (less than 4X4) and where your succah would be permanent like a house (above twenty amos). Or, if your succah is built greater than 4X4 amos your succah would necessarily be permanent like a house (greater than 4x4 amos) and like a house built temporary similar to a succah (less than 20 amos).
The final result being that the words בית and סוכה in the Torah are stripped of any material relevance in terms of קבע and עראי and comes to represent abstract measurements that equate to the mental state of a person perceiving this world as their permanent or temporary dwelling.
It is significant that the Torah represents a בית as the two dimensions of length and width (area) to further illustrate that man naturally stands on the earth and horizontally sees what is in front of him and at his side and begins to think that this world and all that he sees with his physical eyes is the point to life. And, he directs his thoughts and heart after it, while neglecting his spiritual obligations. The remedy provided by the Torah is the mitzvah to dwell in a succah which has the power to bring the spiritual dimension of height (succah) down into our two dimensional lives (House) where we can all declare together: קָדושׁ קָדושׁ קָדושׁ ה' צְבָאות מְלא כָל הָאָרֶץ כְּבודו כְּבודו מָלֵא עולָם
It would seem that Mescestes Sukkah is an instruction manual on how to build our minds into a Beis Hamikdash from which we can connect to and properly serve Hashem.