Perhaps the mishna can be explained based on another line of thinking. The mishna indicates that one day yom tovim such as shavuos, r"h and y"k may have a "shabbos" status rather than regel. The nimukei yosef explains the rationale is that regel should really be no better than shabbos, meaning it should count toward shiva but not stop it. But, since pesach and succos are 7 days, even if they count toward aveilus they will end up stopping it. Based on this logic, even the chachamim may hold that we don't want to distinguish between one regel and another so we allow even shavuos to stop the aveilus. According to this line of thinking shabbos and Regel are exactly the same (except for the private things such as relations and studying torah, that is assur on shabbos but is mutar on regel). If aveilus began before then shabbos and regel "count" but by regel (pesach and succos) that translates into stopping the shiva (and lo p'lug for shavuos). But, if the burial takes place only during the regel then the regel doesn't even count toward shiva and the same would be true by shabbos, just that there is never a burial on shabbos.
However, regarding regel stopping the sheloshim, the gemara implies that the logic is totally different. Really regel should count toward 30, but not stop it. But, since we allow grooming for kavod haregel on erev yom tov, "ho'il v'hutra hutra" - once we allow violation of sheloshim, we don't want to go back and assur it. That is why rav and rav huna insist that one must take advantage of the heter to shave in order to abolish the sheloshim, whereas r' sheishes/abah shaul would say that even if you didn't take advantage, since it was mutar we don't go back and assur it after the regel.
