I would have Scripturally based concerns for the arrangement you discussed, which would be as follows:
- One Pastor - Even though you did not mention it, I understand the Bible to teach that a multitude of elders (synonymous with pastors, shepherds, bishops, overseers, and presbyters) must serve. A single elder, or pastor should never serve. The apostolic pattern is always for a plurality of elders:
Luke wrote:And when they had preached the gospel to that city and made many disciples, they returned to Lystra, Iconium, and Antioch, strengthening the souls of the disciples, exhorting them to continue in the faith, and saying, "We must through many tribulations enter the kingdom of God." So when they had appointed elders in every church, and prayed with fasting, they commended them to the Lord in whom they had believed. (Acts 14:21-23)
Everywhere you find elders mentioned in the Scriptures, you will find them mentioned in the plurality - Phillipi (Philippians 1:1-2), Asia Minor (Acts 14:21-23), Ephesus (Acts 20:17, 28-29), Jerusalem (Acts 15:2-6), "elders in every city" (Titus 1:5), "elders who are among you" (I Peter 5:1-5), etc.. Not only does this accord with good sense (Ecclesiastes 4:9-12 - strength in numbers, resistance to corruption, etc.), more importantly it is the New Testament pattern. This would be my primary concern above the other, because it suggests a deviation from the Bible pattern at the very heart of the leadership.
- Authority of Office - Some authority and decision making power comes with the office of deacon. This is inherent in any office. If these teams are to be legitimate, they must not have any true decision making power; otherwise, they become a third office, which Jesus never appointed (Ephesians 4:10-11; I Timothy 3). This would be one point at which they would violate the organization of the church - creating a new office.
- Reduction of responsibility - Should not every able-bodied, spiritually mature person be involved in visitation, benevolence, encouragement, and membership! These are not works I would expect deacons to oversee, because they are so central to the health of the church. I would expect the elders to oversee and be intimately involved in these works. Regardless, are these teams specializing the membership, relieving shared responsibilities from certain members? Are some members doing all the visiting, while no body else has to worry about it? Is each team specializing, such that other members are able to neglect their share in the other teams' works? This should be answered according to a practical reality, not an ideal situation that would likely not materialize. I can't say this is wrong, so much as it just seems unwise.
- Women leading men - As you mentioned earlier, the Scriptures clearly teach against women serving as elders or deacons (I Timothy 3:1-13; Titus 1:5-11). They also teach against women asserting leadership over men. Would these teams involve women praying over men, teaching over men, instructing over men? Is this an attempt to make use of a loop-hole to put women in the effective place of deacons, serving where God did not intend (I Timothy 2:9-15; Titus 2:3-5; I Timothy 5:3-16)? Also, are these teams being appointed and directed outside the authority and guidance of the elders, or men of the church? If there are enough men to arrange a business meeting of men to discuss and direct these topics, then why can they not lead the works?
There is nothing to say that women cannot serve, or minister in the work of encouragement, visitation, admonishment, Lord's Supper preparation, etc. The woman's place is not a place of public, authoritative leadership. However, a godly woman commands a tremendous influence, when she indirectly leads by an example of service. Her obligation and privilege to serve is as important, real, and necessary as that of the man. The only difference is in the form of service, not the magnitude or criticality.
Now, I am not saying that all "teams" or "groups" are unscriptural. We have "groups" at the church, which I just left, but each group was responsible to visit, encourage, assist, and see to the needs of people in their group, as well as the whole church. We divided into smaller groups, just to fight the "big church" syndrome. This facilitated getting to know each other better and dissolving social barriers. There was no responsibility given uniquely to each group. No power or authority was given to each group. We also mixed up the groups every few months. Also, the groups typically focused on activities outside of the assemblies. The boundaries of the groups were transparent. The responsibilities were shared among all members, not groups. There was no authority given to the groups. I would have no problems with such groups, any more than divided Bible classes. The question is one of authority and function: Do these teams command authority that is not rightfully their own? Are these teams doing work in which all members should be involved?
I know you are not in a strong position to directly change this, but my primary concern would be, "Why are there no men qualified to be deacons, much less additional elders?" If a church is new, then that is expected, but if it is established, then why is not bearing fruit in producing strong, male, Christian, leadership? Such situations call for strong, Scriptural teaching and passionate persuasive attempts for hearts and homes to change, such that qualified men may grow into place. If God's pattern is followed, these gifts should be available to the church (
elders, deacons, teachers, etc - Ephesians 4:10-16). Has teaching and discipline not been "meaty" enough to produce mature Christians (
Hebrews 5:12-14), or has materialism (
Matthew 6:19-24; 13:1-23; II Timothy 2:3; I John 2:15-17) and toleration of wickedness been allowed to abide (
I Corinthians 5:1-3; 15:33-34; II Corinthians 6:14-7:1)? I am sure you are already sensitive to these points, else you would not have been concerned to even write; however, I wanted to provide this for additional meditation. What is being done to fix the real problem, of which the lack of deacons is only a symptom?
I have not been confronted with this exact situation, so my thinking is not as crystallized on this scenario as it is on some other topics, even ones related to church organization. Consequently, with additional prayer, study, and meditation, I may refine or redirect these thoughts, but hopefully this will provide you something to consider during this upcoming selection.
You and the church where you are will be in my prayers. May God bless you such that His will is evident and cherished.