What is an overview of teachings of Messianic Jewish Christians regarding circumcision?

The overview of Messianic Judaism or Messianic Christianity about circumcision can be understood from their statement of beliefs that you quoted. Circumcision is an essential part of being Jewish or a Jewish lifestyle, so is the observance of kosher diet. Their practice of continuation of the Jewish practices does not violate Paul's instructions to the Gentile new believers of Galatians as he also instructed that circumcision or non-circumcision doesn't matter but only keeping of the commandments. The instructions to Galatians against circumcision therefore apply against mandatory observance of it as an essential practice for salvation. Thus if the Messianic believers wants to continue Jewish traditions and lifestyle as a non-mandatory cultural significance then it is permissible by Paul.

(1 Corinthians 7:17-20) 17 Only let each person lead the life that the Lord has assigned to him, and to which God has called him. This is my rule in all the churches. 18 Was anyone at the time of his call already circumcised? Let him not seek to remove the marks of circumcision. Was anyone at the time of his call uncircumcised? Let him not seek circumcision. 19 For neither circumcision counts for anything nor uncircumcision, but keeping the commandments of God. 20 Each one should remain in the condition in which he was called.

Since the author of the question is seeking a general overview and not the view of specific congregations--I will offer an answer similar to Michael16, which is not itself wrong, but does lack specificity.

Right now there are two major branches of official Messianic Judaism. Those branches are the MJAA and the UMJC. The former being the body which started first and the later, a breakaway movement, and as such the UMJC is more stringent in their observance, if only in their own view.

A google search of UMJC and Circumcision yields the following link: https://www.google.com/search?q=UMJC+circumcision

The first result (in my search) then becomes immediately relevant: Is Judaism Jewish? Early on (in the third paragraph of said document) the author, one Dr. Mark Kinzer, speaks of the same proof text Michael16 did: 1 Corinthians 7:18, 19. Kinzer states:

"but keeping the commandments of God." Paul acknowledges with these words that the Torah commands Jews to be circumcised and to keep the mitzvot given to Israel, but expects non-Jews to keep only those commandments given to all human beings. Thus, what matters is not being Jewish or non-Jewish, but obeying those Divine commandments that apply to us.

Since the site bares the markings of the UMJC we can take this as an official position and not one individual congregation.

Next we come to the more lax MJAA.

Putting the terms, MJAA IAMCS Circumcision into a google search bar yielding the following results: https://www.google.com/search?q=MJAA+IAMCS+Circumcision

It should be noted that the results for the second search performed is far fewer than the first for the very reason that the MJAA has a less concrete positon on the matter than does the UMJC.

Quoting from a document among the results:

The main Jewish life cycle events include circumcision, bar/bat mitzvah, wedding, and death and each of these events have their own set of liturgy and ritual. The first two are pertinent to this study. In obedience to God’s command to Abraham, Jewish males are circumcised on the eighth day as a physical sign of the covenant God made with Abraham in Genesis 17:11-12. (Messianic Jewish Liturgical Practices, by Elizabeth Ames, p. 10)

The only other relevant quote comes from Rabbi Jim Appel, a messianic Rabbi from New York whose congregation Shema Yisrael belongs to the IAMCS. This becomes relevant because when understanding his quote and how the IAMCS works, he would not be a member of that organization if his beliefs did not match theirs. (The IAMCS is the governing body of the MJAA.)

A substitute document is Competing Trends In Messianic Judaism: The Debate Over Evangelicalism, which cites congregation Beth Yeshua as a forerunner for the MJAA position (though certainly progressive in its implementation). This article may be the best fit for your desire for an overview of Messianic Judaism as a whole as it does, like I have here done, break the movement into its two constituent bodies.