I had proposed that, according to R' Yochanan, the Mishnah could work according to either R' Yehudah or the Chachamim.
According to R' Yehudah, the reason a Na'arah cannot accept her divorce/marriage document is because "two hands cannot accept as one." If a Na'arah has no father, perhaps he would hold that she could accept on her own behalf, as there are not two hands able to accept.
According to the Chachamim, the reason a Na'arah cannot accept her marriage document but can accept her divorce document is because, as per Kiddushin 44a,
קידושין דמדעתה אביה ולא היא גירושין דבעל כרחה בין היא בין אביה
Marriage, which works with her consent – her father, and not her. Divorce, which works against her will – whether her or her father.
As Rashi explains,
אביה ולא היא - שהתורה זיכתה לו
"Her father and not her" – for the Torah granted it to him.
This is an intriguing term, to "grant" it. Perhaps according to the Chachamim, the right belongs to the Na'arah, but if she has a father, the right is transferred to him. If she doesn't have a father, as in our case, the right isn't transferred to him and remains with her.
I was hesitant to say for certain that this is a correct approach to answer the question, but I recently discovered evidence that seems to support my claim.
A practical difference as a result of my interpretation of the Chachamim is that while this halacha would apply to a girl who never had a father, if she was orphaned after birth, perhaps she would not be able to accept her Kiddushin until she matures. Indeed, this seems to be the approach of the Mordechai cited by the Rema (EH 37:13):
נתקדשה לדעת אביה ונשאת שלא לדעתו בין שאביה כאן בין שהלך למדינת הים אינם נשואין [...] הגה וי"א דה"ה אם מת האב קודם שנשאת ונשאת (כן משמע במרדכי פ"ב דקידושין בשם מקצת רבותינו):
If she did Kiddushin with her father's consent and did Nisuin without his consent, whether the father is present or went overseas, it is not Nisuin. [...] Rema: Some say that this is the halacha if the father died before she did Nisuin, and then she did Nisuin (thus is implied in the Mordechai in the second chapter of Kiddushin in the name of some of his Rabbeim).
The Be'er Heitiv quotes the other opinion in the Mordechai, which leads to an alternative understanding of the Chachamim's opinion according to R' Yochanan:
ומסקנת המרדכי דהוי קדושין מעלייתא מאחר דאב מת ואין חשש שמא ימחה ב''ש:
And the conclusion of the Mordechai is that the Kiddushin is effective after the father dies.
According to this approach, it's not just that the right is not initially transferred to the father, but that it's transferred back when he dies!
This understanding of the Chachamim seems to be shared by Rabbeinu Tam, as cited by the Chelkas Mechokek:
עיין שם שרבינו תם תמה על דבריהם והאריך להוכיח דאין האחים יכולין למחות ואין אדם מוריש זכות בתו לבניו
See there that Rabbeinu Tam is astonished on their words, and he discusses at length to refute them. [He argues] that the brothers are unable to protest, and a man cannot bequeath the rights regarding his daughter to his sons.
This, too, implies that the right reverts to the daughter, rather than being a right which the father can keep, as if the father keeps it, her brothers would be able to protest.