To me "even as" means just like Jesus or exactly like Jesus. Husbands are the head of the house. Not in a domineering way, but in a leadership way. The husband should be like a prophet of the house, the leader who leads his family into godly ways.
Not one scripture makes the man "head of the house". There is one that makes the woman "house despot": Titus 2:5. The Greek word is οικουργους. And Titus was written as specific instructions on how Titus should set up the community of believers on the island of Crete, where the men were lazy and the women were shirking home responsibilities. Paul was not telling the women to submit better to the "lazy" men but to take charge of their homes.
As for a husband being the head of his wife, Paul used the body analogy to denote unity, not a chain of command; see Eph. 4:16 and Col. 2:19. Head never meant boss or authority in either ancient or koine Greek. The closest meaning to that was the "head" of an attacking force, which again did not mean the general but simply the leading point of the attacking force. Greeks believed that the body grew out of the head and was thus the source of the body. Yet the head and body were mutually dependent: the head fed the body, but the body supported and transported the head.
Paul went on to describe the husband/wife relationship as mutually submissive; see 1 Cor. 7:4 and Eph. 5:21. And in the passage you mentioned, 1 Cor. 11, Paul ended it with vs. 11-12: "Nevertheless, in the Lord woman is not independent of man, nor is man independent of woman. For as woman came from man, so also man is born of woman. But everything comes from God."
Now to Gal. 3:28. It clearly says what the situation is for those already "in Christ", not who can become "in Christ". Also, even before Christ, slaves and Gentiles and women could be "saved". Would anyone claim that Gentiles are not to be treated equally in the Body of Christ? Would anyone claim the same for slaves? Then there is no reason to make an exception for women. As Paul taught about the parts of the Body, no part rules over another part, and even the parts that are considered the weakest should be treated with special honor (1 Cor. 12:23-24).
I have written an entire book on this issue, but this is just off the top of my head (an expression having nothing to do with authority). Teachings have consequences, and few have had as much harmful effect upon Christian women than the idea that men should rule over them, however benevolently. It denies the fully autonomy and personhood of women, even if only symbolically or in some kind of "role playing" manner. But this is a huge topic for another day.