[See part one. We are looking at 3 ways to harmonize the 3 “conflicting” passages in the Pauline epistles about women.]
Another way to harmonize these passages is to make a distinction between authoritative and non-authoritative ministry in the church. Edmund Clowney represents this type of view in his book on the church* specifically in the chapter entitled “The Ministry of Women in the Church.” This view makes the 1 Timothy 2 passage paramount. Men are to be the authoritative leaders of the church, and women should not be involved in ministry that would impinge on this role. Clowney states that women can teach in a variety of informal circumstances (such as teaching adult Sunday school, and including teaching men) as long as the teaching is not authoritative or disruptive to the “biblical order” of the church.
In regards to harmonizing this with the passages in 1 Corinthians 11 and 14, since prayer is not bringing God’s authoritative word to the church, women can participate through prayer in church services. Women can likewise prophesy as long as deference is made by the women to male leadership in the church. Clowney interprets 1 Corinthians 14:34 to refer to women being silent when an authoritative decision must be made about a prophecy. (Only men could judge a prophecy.)
This harmonization view handles the Scriptures more consistently than option one, and I can tolerate this view even though I respectfully disagree. The problem is that while some evangelicals may hold a view similar to this one, it does not seem to play out in the life of the church. It gets lip service, but what actually happens is an option 1 scenario. I have rarely seen women able to open or close a church service in prayer, able to share a prophetic word, or do informal teaching (such as teach an adult Sunday school class) if both men and women are present. Women are most often restricted to singing in the church service, sequestered off with other women or children to use their gifts, or limited to administrative/hospitality roles. [Note that I am sharing my personal observations, and the area of the US that I live in seems more strict than some other areas of the US.]
Despite more consistency with this harmonization, some critique must be offered of this or similar viewpoints. For a full critique of interpreting the 1 Timothy passage as Clowney does (women must not have authority over men), see this post where I have already expounded on it. This passage can be seen as dealing with a unique cultural situation, and the authority being prohibited was an inappropriate domineering authority.
Craig Keener makes an astute observation regarding the interpretation of 1 Corinthians 14:34 as referring to women not judging prophecies. If this is the correct way to interpret it, how is it that “judging a prophecy” is more authoritative than sharing the prophetic word itself??  The text does not indicate this fact. One could easily consider the sharing of a prophetic word to be more authoritative than the discerning judgment of it, or at the very least the sharing and judgment would be on a similar level of authority! There seems a rather arbitrary aspect to deciding what is authoritative or non-authoritative.
In Paul’s lists of spiritual gifts, prophecy is mentioned at the highest level, second only to apostleship (1 Cor. 12:28; Eph. 4:11). Teaching is listed third in the 1 Corinthians 12 listing, and prophecy is also grouped with teaching, revelation, and knowledge in 1 Corinthians 14:6. According to 1 Corinthians 14:1 prophecy should be desired more than the other gifts. The point being made is that if women could prophesy, little else should be prohibited for them! Bilezikian summarizes that if women
…had access, under apostolic sanction, to the highest levels of ministry in the early church then equivalent ministries should likewise be accessible to women in the modern church [emphasis added]. 
In regards to teaching, where is that line between authoritative and non-authoritative? Again, there seems a rather subjective aspect to the decision. This can even drift into lengthy legalistic lists. Wayne Grudem has divided church activities into 3 lists of 83 items based on authority in regards to what women should or should not do in the church. To be quite frank, it seems reminiscent of the oral codes of pharisaic Judaism! 
Personally, I consider all teaching to be authoritative! Scripture indicates that teaching is a serious responsibility (James 3:1), and accurately handling the Word of God is critical (2 Tim. 2:15). It seems the greater concern should be that a teacher has the gift of teaching and is adequately trained in the Scriptures, but in some circles the gender of the teacher has become the greater issue. Sadly, I have observed cases where a man who clearly did not have the gift of teaching nor adequate training was put in charge of an adult Bible class, while a woman with the gift of teaching and training could not lead it simply because of her gender. The whole Body of Christ suffers as a result!
Men and women together reflect the image of God, and need one another. Men need to hear women teach, and women need to hear men teach. Indeed, this would be reflective of the early church where all were coming together and all were using their gifts in a mixed sex setting.
(Part 3 here.)
* Clowney, Edmund C. The Church. Downers Grove, Illinois: IVP, 1995.
 Ronald W. Pierce, and others, eds. Discovering Biblical Equality (Downers Grove: IVP Academic, 2005), 163.
 Gilbert Bilezikian, Beyond Sex Roles (Grand Rapids: Baker Academic, 2006), 107.