I am a Cohen, and Min Hadin ( since I am a partner in the animal ) no Matnas Kehuna is required. But we saw in the Gemaruh, that although the Novieh Yekezkel was also a Cohen, he was Machmir not to eat meat unless Matnos Kehuna was taken.
a) Is there such a Halacha to be Machmir ( as we see by Mesucenes, and Horat Chochom ) ?
b) and if so, do we have to give it to another Cohen, or can I take it as Matnas Kehuna ?
Clearly Yechezkel was not talking about his own animal, for then he is Patur, but rather a Yisrael's animal, which is Chayav. As for what Rashi writes, see Shitah Mekubetzes who omits that Girsa.
The Matanos do not make an animal Tevel like Terumah makes fruit Tevel. Therefore, actually even a Yisrael can eat the meat before Haramah of the Matanos. See the Gemara in Chulin 132b that relates that Rabah bar bar Chana in the name of Rebbi Yochanan compares it to Tevel, and the conclusion is that it is Mutar, and therefore Yechezkel's comparison of the Matanos to Tevel was a Chumra. (While it seems that the Halachah of Rebbi Yochanan is mid'Rabanan, Tosfos here (DH she'Lo) implies that it is mid'Oraisa.
D. Zupnik