Chanania and perek 3 of Shabbos - if yeish bishul acher bishul

Question

How do we “find our hands and feet in the beis midrash”?

1. We seem to poskin that yeish bishul achar bishul for food that is ma’achal ben drusai; if so, cooking it on Shabbos would be forbidden and perhaps chayav chatas (Rambam, Shulkhan Arukh 318).
2. Ashkenazim poskin like Chananya ["להחזיר תנן"] on the first Mishnah in the third perek. Sefardim don’t, but they also at least have to be able to read the Mishnah according to Chananya. According to him, the Mishnah says (actual Mishnah words in bold), “…If heated with peat or wood, [you may do shehiyah (with food that is ma’achal ben drusai), even if the kirah is not garuf or katum. But,] you may not do chazarah unless the kirah is garuf or katum.”
   The simple reading surely is that, if the kirah is garuf or katum, chazarah is permitted with food that is ma’achal ben drusai. (Otherwise, the Mishnah would be changing the case in the middle.)
3. All rishonim (except for Rashi) seem to hold that garuf v’katum doesn’t stop the kirah from cooking, but serves as some kind of a heker or barrier, preventing the person from stirring the coals. Or, that without garuf v’katum, it “appears to be cooking” (מחזי כמבשל). But all these rishonim hold that a kirah that is garuf v’katum is still fully capable of cooking.

So how is possible to read the Mishnah according to Chananyah?

By the way, the same question seems to apply on the beginning of the mishnah: With קש וגבבה (straw and stubble), you may "place" food on the kirah. According to Chananya, that means doing chazarah [להחזיר תנן, unless he's changing in the middle of the mishnah], and with food that is מאכל בן דרוסאי, only partially cooked. How is that possible, if the straw and stubble add enough heat to cook?

The simple part of the answer is that all the Rishonim we usually see explaining the gemara (Tosefos, the Ramban, the Rashba, the Ran) - every one holds that אין בישול אחר בישול, so none of them has this issue. On the contrary, this is pretty much their source that אין בישול אחר בישול, these kind of reading issues. Then they have the opposite issue: Why then is there any problem with chazarah, if the food is cooked? They need to come up with various kinds of reasons d'rabanan.
So my question is based on, if you hold יש בישול אחר בישול.

Answer 1

Eglei Tal in Melechet Ofeh 10:10 is bothered by this question. He writes that it is clear from the mishnah at the beginning of perek kirah that once a food reaches the level of ma'achal ben derusa'i there cannot be bishul mide'oraita, as otherwise how could chazara be permitted?

His solution is to posit that according to the majority of rishonim (he lists Tosafot, Rosh, Tur, R. Yerucham and Rambam) there is no prohibition to cook food which is ma'achal ben derusa'i on a de'oraita level, but that there is still a prohibition miderabbanan. Since we are only dealing with an issur derabbanan, chazara is permitted lechatchilah, providing one fulfils the relevant conditions. (ibid. 10:15-16)

Answer 2

I don't think this is the answer, but I would point out that the Beis Yosef OH 253 brings a Rishon who gets around this question.

או"ח סי' רנ"ג ד"ה ומ"ש רבינו כל זמן כו' וכתב עוד בשם הר"י דהא דשרי להחזיר דוקא כשהגיע מבע"י למאב"ד אבל אם לא הגיע לא יחזיר אם נטל עכ"ל

This Rishon says that you can do chazarah, but the food must be מאכל בן דרוסאי while it's still day. The Beis Yosef is hard-pressed to find a reason for the din, as the chazarah happens later on Shabbos.
I'm wondering if this Rishon is coming to answer my question: He holds that you aren't allowed to cook food that's partially cooked on Shabbos, so Chananya must be talking about fully cooked food. How then does he read the mishnah allowing chazarah on מאכל בן דרוסאי (if the kirah is garuf v'katum)? The state of the food before Shabbos - the same as the food needs to be to allow shehiyah without garuf v'katum.