This is going to take more than one post. But let me make a start. It's worth repeating that I am convinced that God has been restoring these gifts (in Ephesians 4:11) to his church over the past 40 years, but I also feel that groups can be too prescriptive about them, and how they should function.
The first thing to point out is that although we use the term 'ministries' for apostles, prophets, evangelists, pastors and teachers, the passage does not do that. It refers to them as gifts (v.9). In fact, they are to prepare, equip or perfect everyone in the church for the work of ministry (v.12). As I am arguing for a less prescriptive approach to the NT, I won't fuss about this; but we must be careful, because the whole idea of having a 'ministry' has become tangled up with getting a position, a recognised leadership role, even a title. And this totally misses the point of the principle here. These gifts are to equip and empower everyone to do the work of ministry/service. They are not superstar 'ministries' for the church to admire; they are to equip the body, not impress it. If we could translate the the word for ministry (diakonia) as we should - service - so that these 'ministries' are seen as servants (along with all in the church), that might help.
Another relevant principle here is that of diversity. It seems to me that one of the key thrusts of this passage.is about the church, the body of Christ, coming to maturity, to the fullness of the stature of Christ (vv.11-13). A mark of maturity is balance, to be well-proportioned, to be whole and complete (v.16). Therefore, diversity is required for maturity. These gifts are not to do with positions or leadership roles in the church. (They may or may not be in leadership; I suggest we should take government and leadership out of the equation.) They are to do with the diverse gifts, perspectives and strengths that the different people bring: prophets help the church to be more prophetic, pastors help it to be more pastoral, evangelists, more evangelistic etc. If one is more dominant it's like a colour TV where one colour only is getting through - the picture is all red, or all green for example.
When we begin to look again at this passage being not about positions but perspectives that each gift brings to bear on the church and its service, we can perhaps make room for a new pattern of how they work in the church to emerge. More on this in my next post, I hope.