I think I must first say that we are never given a precise plan, identified as Paul’s strategy.
I think as we look back, we can see that there is a strategy, but I’m inclined to attribute this more to the Spirit of God and the Sovereign hand of God than to the church, or to Paul.
As I read the Book of Acts, I am impressed by the fact that God seems to be doing much of His work in spite of the apostles. The apostles choose Matthias as Judas’ replacement (Acts 1), even though they were instructed to wait for the coming of the Holy Spirit (Acts 1:4-5). We never hear of Matthias again, and yet Paul seems to be God’s choice as the 12th apostle, in spite of the fact that the apostles initially resist meeting with him (Acts 9:26-28). When the church is scattered, the apostles remain in Jerusalem. They are not at the forefront of evangelism, and it is those who are unnamed and unknown who blaze the trail (see Acts 1:8; 8:1-2; 11:18-21). Indeed, when Peter is summoned to the home of Cornelius and these Gentiles come to faith (Acts 10), the Jewish Jerusalem leaders call Peter on the carpet (Acts 11). The apostles appoint deacons, so that they can devote themselves to the ministry of the Word and Prayer (Acts 6), and yet it is two of these deacons who set evangelism and preaching in motion - Stephen, by his death (Acts 6-7), and Philip (Acts 8).
The first missionary journey begins in Acts 13, and it is the Holy Spirit who sends Barnabas and Saul out. Paul wants to make a second missionary journey, which is essentially re-visiting the places he and Barnabas first visited (Acts 15:36). It was an argument between Barnabas and Paul that divided this team into two teams (I don’t think either man was wrong), and it was the sovereign guidance of God that led Paul to Philippi (16:6ff.).
All of this does not look like Paul’s strategizing as much as God’s guidance. No one devised the strategy of Paul getting arrested, and eventually arriving in Rome.
Well, that’s my take on the matter. I lean more heavily on divine guidance and direction here, and less on strategy. That is not to say that strategy is wrong, or forbidden. It is to say that I don’t think we see a lot of Pauline strategy in Acts.