Answer

On your understanding, this would create a contradiction in Maimonides, who rules like Rabbi Shimon in both places: Laws of Sacrificial Procedure 17:9; Laws of Slaves 7:2.
I do not see a connection between the two passages. In the Mishnah in Peah (see Gittin 8b, near the end), the issue is splitting a statement—that is, accepting part of the master’s words (regarding the slave) but not the rest (regarding the land). And even the Sages, who disagree with him, simply interpret the master’s words differently: since he did not say “yourself and my property,” it is clear that he only meant to flatter the slave so that he would work better.
But in the Mishnah in Menachot, the question is entirely different. There Rabbi Shimon says that if he did not vow in the normal way that people make vows, then it does not take effect. There the discussion is about his intention, not about splitting a statement. Rabbi Shimon argues that his intention was not to make a vow.
One could further distinguish between them in many ways as well (freeing a slave is a forbidden act, and it also causes a loss to the master, who loses his slave). But as I said, I do not see any difficulty here that requires distinctions in order to resolve it.