Let me break this down by question:
1. Are there any documented halachik authorities that rule that the belief in a dead Messiah is beyond the pale of permitted Jewish belief and therefore would qualify as Kfira?
Short Answer: Yes -- and we do consideer it kfira in the case of Jews who adopt Christianity.
Rabbi Gil Student, in his book Can The Rebbe Be Moshiach? Proofs from Gemara, Midrash, and Rambam that the Rebbe zt"l Cannot be Moshiach, brings down various sources that demonstrate that the belief in the Rebbe as Moshiach violates halacha and could be considered heresy. Largely, Rabbi Student's book relies on the Rambam's set of legal requirements to establish whether one is moshiach or not. In Chapter 4, Rabbi Student quotes Rambam's Mishneh Torah, Hilchos Melachim 11:4:
If a king will arise from the House of David who delves deeply into the study of the Torah and, like David his ancestor, observes its mitzvos as prescribed by the Written Law and the Oral Law; if he will compel all of Israel to walk in [the way of the
Torah] and repair the breaches [in its observance]; and if he will fight the wars of G-d –he is presumed to be Moshiach. If he succeeds in the above, builds the Beis Hamikdash on its site, and gathers in the dispersed remnant of Israel, he is definitely the Moshiach. He will then perfect the entire world, [motivating all the nations] to serve G-d together, as it is written (Zephaniah 3:9), "I will make the peoples pure of speech so that they will all call upon the Name of G-d and serve Him with one purpose."
At Hilcohos Melachim 11:5, Rambam says:
But if he did not succeed in all this or was killed, he is definitely not the Moshiach promised in the Torah... and G-d only appointed him in order to test the masses.
Rabbi Student's book also cites the Ramban's famous disputation of Christian belief that their Jesus was the Moshiach by simply pointing to the fact that the ultimate proof that someone was or is the Moshiach would be the fact that we're living in the Messianic Age with no wars and 100% of the world believing in the G-d of Abraham. See Kisvei HaRamban vol. 1 p. 311). The presumption of Ramban's view is that once the claimant to the title of Moshiach dies, the claim dies with him. Using this analysis, all authorities are agreed that it is heresy for a Jew to accept Jesus as the Moshiach.
2. Have the rabbis specifically declared that Chabad meshichists are guilty of heresy that would, for example, make it inappropriate for one to rely upon the shkitah of a meshichist Chabadnik? (quesiton restated)
Short answer: So far, while there have been rabbis who have declared the view to be wrong and not a part of Judaism, see e.g. Rav Aaron Feldman's view with respect to removing oneself from a minyan where the prayer leader inserts meshichist phrases into the avodah. But, as Rabbi Student points out, and which collections of statements on the subject agree, there is no organized effort to declare Chabad meshicists as heretics; rather the rabbis appear to have left the door open for meshicists to comeback into the Orthodox Jewish mainstream as their views soften.
Chapter 6 of Rabbi Student's book, generally, demonstrates how one could argue today seeks to make the case that belief that a dead man can be moshiach, still, is apikorus. Go to the link I've provided for the details of his analysis which, again, relies on the Rambam -- specifically his commentary to the Mishna in Sanhedrin 10:1 where he lays out his 13 principles of faith. He concedes that there is no organized effort to declare meshicists to be heretics.
The opinions of various contemporary gedolim -- before and after the Rebbe's death -- can be found at Wikipedia under Chabad Messianism. There you can see condemnation of the concept, but reluctance to expel the Jews who hold mistaken views.
The language you use, that Rabbinic sources suggest that belief that the Rebbe could still be the Moshiach is not "beyond the pale," has been attributed by meshichists to 1996 statement by Rav Aaron Solovechik in contradiction to his view stated two years ealier that the Rebbe cannot be moshiach because he's dead. A subsequent letter resolves the conflict. In it, he states:
"To my great dismay. . . publications affiliated with the Lubavitch movement have persisted in stating that I validate their belief that a Jewish Messiah may be resurrected from the dead. I completely reject and vigorously deny any such claim. As I have already stated publicly. . . such a belief is repugnant to Judaism and is the antithesis of the truth. My intent in signing the original letter . . . was merely to express my opinion that we should not label subscribers to these beliefs as heretics. Any statements in that letter which imply an endorsement of their view were not shown to me at the time I signed and I once again repudiate any such ridiculous claim."
3. Additionally, what do they purport to do about the prevalence of Chabad shochtim who do hold this belief? Do they hold their shchita to be invalid? Would they not join them in a minyan?
Some rabbinic organizations have taken a strict view with respect to giving hashgacha to restaurants that promote the view that the Rebbe will return as Moshiach. A New York restaurant supervised by Rabbis Marc Angel and Avi Weiss in 2002 threatened to withdraw hasgacha from the restaurant for describing the Rebbe in its menus as "MHM" (i.e. Melech HaMoshiach). However, I haven't heard or seen any cases like this thereafter.
