Eiruvin 81 - Fixing the Bread with a Toothpick

The gemara talks about using a broken loaf for an eiruv. The gemara says that if it is missing the shiur challah which is 1/24 for a ba'al habayis and 1/48 for a baker it is still considered whole. The Gaon Yaakov explains that the gemara is not allowing the loaf to be missing up to 1/24, rather the gemara is saying that if it was taken for the mitzvah of hafroshas challah, then it is allowed to be missing up to 1/24 for a ba'al habayis and up to 1/48 for a baker. Another halacha that the gemara mentions is that one can reattach the missing piece using a toothpick provided that he does a good job and it isn't obvious that it has been broken.

Do these halachos also apply to lechem mishna on shabbos?

The Sha'arei Teshuva 274:1 cites the chacham tzvi 62 who says that if the lechem mishna is missing a piece it is dependent on a machlokes R"I and Rosh. The R"I cited in Tosafos holds that even missing the smallest amount doesn't qualify as a shaleim for eiruv unless the missing piece was taken for the mitzvah of challah, and the chacham tzvi assumes that the same applies to lechem mishna. Whereas the Rosh holds that so long as it is missing less than the shiur challah, even if not taken for the mitzvah of challah, it still qualifies as a shaleim for eiruv (so long as it is missing less than challas nachtom which is 1/48) and the chacham tzvi assumes that the same would apply to lechem mishnah.

According to the approach of the Chacham Tzvi that we can learn halachos of shaleim by lechem mishna from eiruv, it would seem that fixing with a toothpick can also be learned from the halacha of eiruv. However, the Maharatz Chiyus writes that by eiruv the reason why it is repairable is that the problem with using a perusah is that it causes eivah, therefore so long as it isn't recognizable that it has been broken because the toothpick repair makes it look like a shaleim, there won't be any eiva. Based on this approach, lechem mishnah which requires shaleim because of chashivus, not just because of eivah, we can't learn from eiruv that fixing with a toothpick is adequate. In truth, even the chacham tzvi ends his teshuva by pointing out that by eiruv the issue is eivah and says that he is being medayek from the mishna that refers to it as a shaleim. Since it qualifies as a shaleim, it should still be a shaleim for lechem mishna also. However, regarding  din of fixing with a toothpick, we don't see that the mishna refers to that as a shaleim, therefore perhaps even the chacham tzvi would agree with the maharatz chiyus that we can't learn that din from eiruv.