Yoma 33 Third Maracha on the Mizbeach

The Gemora on Yoma 33a states that there were two fires on the mizbeach every day - one called 'maracha gedola' which was used for all the burnings of the meat (Rashi) and one for the ketores. There actually was a third one as well, as stated on daf 45a according to Reb Yosi that was there to fulfill the requirement of the Torah to have fire on the mizbeach at all times. Rashi (ibid) says that if there was not enough fire on the maracha gedola, it would be replenished from this one. The Rambam does not mention this halacha. The Chinuch (mitzva 132) states that this third fire is an integral part of the mitzva and if the kohanim kindled the two first, but not this one, they were mevatel the mitzva. The Meiri (here and on daf 45) comments similar to Rashi, however in Tamid 29a, he states that the third fire had no use whatsoever except to fulfill the requirement of having fire on the mizbeach.

I was wondering, do the Rambam and the Chinuch (and Meiri in Tamid) disagree with the halacha of Rashi, that if fire was needed for the maracha gedola, it could not be taken from this fire? What would be done?