Berachot 14b: Tefillin before Shema or after it?

Consider the following, in Berachot 14b:

רב משי ידיה וקרא ק"ש ואנח תפילין וצלי והיכי עביד הכי והתניא החופר כוך למת בקבר פטור מק"ש ומן התפלה ומן התפילין ומכל מצות האמורות בתורה הגיע זמן ק"ש עולה ונוטל ידיו ומניח תפילין וקורא ק"ש ומתפלל הא גופא קשיא רישא אמר פטור וסיפא חייב הא לא קשיא סיפא בתרי ורישא בחד מ"מ קשיא לרב רב כרבי יהושע בן קרחה סבירא ליה דאמר עול מלכות שמים תחלה ואח"כ עול מצות אימר דאמר רבי יהושע בן קרחה להקדים קריאה לקריאה קריאה לעשיה מי שמעת ליה ותו מי סבר ליה כרבי יהושע בן קרחה והאמר רב חייא בר אשי זמנין סגיאין הוה קאימנא קמיה דרב ומקדים ומשי ידיה ומברך ומתני לן פרקין ומנח תפילין והדר קרי ק"ש וכ"ת בדלא מטא זמן ק"ש א"כ מאי אסהדתיה דרב חייא בר אשי לאפוקי ממ"ד למשנה אין צריך לברך קמ"ל דאף למשנה נמי צריך לברך מ"מ קשיא לרב שלוחא הוא דעוית:

Or, in English:

Rab once washed his hands and recited the Shema' and put on tefillin and said the tefillah. But how could he act in this way,⁹  seeing that it has been taught: 'One who digs a niche in a grave for a corpse is exempt from reciting Shema' and tefillah and from tefillin and from all the commandments prescribed in the Torah. When the hour for reciting the Shema' arrives, he goes up and washes his hands and puts on tefillin and recites the Shema' and says the tefillah?' Now this statement itself contains a contradiction. First it says that he is exempt and then it says that he is under obligation? — This is no difficulty; the latter clause speaks of where there are two,¹⁰  the former of where there is only one. In any case this seems to contradict Rab? — Rab held with R. Joshua b. Korhah, who said that first he accepts the yoke of the kingdom of heaven and then he accepts the yoke of the commandments.¹¹  I will grant you that R. Joshua b. Korhah meant that the recital [of one section] should precede that of the other. But can you understand him to mean that the recital should precede the act [of putting on the tefillin]? And further, did Rab really adopt the view of R. Joshua b. Korhah? Did not R. Hiyya b. Ashi say: On many occasions I stood before Rab when he rose early and said a blessing and taught us our section and put on phylacteries and then recited the Shema'?¹²  And should you say, he did this only when the hour for reciting the Shema' had not yet arrived — if that is so what is the value of the testimony of R. Hiyya b. Ashi? — To refute the one who says that a blessing need not be said for the study of the Mishnah;¹³  he teaches us that for the Mishnah also a blessing must be said. All the same there is a contradiction of Rab?¹⁴  — His messenger was at fault.¹⁵

Thus, the conclusion of the setama degemara in Bavli is that this witnessed behavior of Rav was a one-off, since his messenger was late in bringing him his tefillin, and so this does not represent a deliberate position.

I don't know how to answer the contradiction posed by the statement of Rabbi Chiyya bar Ashi about Rav's common conduct.

But I do know that the parallel Yerushalmi also contrasts Rav with the brayta, puts him in accord with Rabbi Yehoshua ben Korcha, and then does not answer that this was a one-off. Indeed, rather than an observed single incident, the Yerushalmi presents it as a statement of Rav, which would then be a deliberate position. Yerushalmi Berachot 13b:

Rabbi Chiyya in this Yerushalmi is presumably Rabbi Chiya bar Abba, rather than Rabbi Chiya bar Ashi.

Perhaps there was a reversal in Rav's conduct somewhere? Certainly we see in Yerushalmi that Rabbi Yochanan is insistent in the order, and thus cognizant that there may be a dissenting opinion, in the form of Rav. And certainly we see in Bavli that Rabbi Yochanan takes a strong position against those who would do this:

'Ulla said: If one recites the Shema' without tefillin it is as if he bore false witness against himself.¹⁶  R. Hiyya b. Abba said in the name of R. Johanan: It is as if he offered a burnt-offering without a meal-offering and a sacrifice without drink-offering.

Read in the context of the dispute between Rav and Rabbi Yochanan in Yerushalmi, this informs me that, despite the setama degemara's erasure of Rav's position and action, there actually was a machlokes between them.

One of the klalei horaah is that in case of dispute between Rav and Rabbi Yochanan, the halacha is like Rabbi Yochanan. So there should be no change in our conduct, on the basis of this.

Related: It is Rabbi Yochanan who is always speaking about the importance of being somech geulah letefillah. Would donning tefillin with its berachot have formed an improper interruption?