Dating the Second Epistle to the Corinthians

The Acts proves to be quite a reliable history of the early Church. Of course, some details would be missing and it would be unfair to demand Luke to be encyclopaedic.
It is well known that the canon of the Bible does not follow the chronological order of when the books were written. That is to say, Matthew might not have been written before Mark and the First epistle to the Corinthians before the Second. However, most scholars agreed that the First epistle to the Corinthians was indeed written before the Second. Furthermore, the Second was likely to be a composite of letter fragments. OK, I think it is a good exercise to try to prove that the First was written before the Second.
Compare the opening verses of the two letters, we can easily see a glaring difference in the co-workers of Paul, Sosthenes in the First epistle and Timothy in the Second.
Paul, called by the will of God to be an apostle of Christ Jesus, and our brother Sosthenes,
To the church of God which is at Corinth, to those sanctified in Christ Jesus, called to be saints together with all those who in every place call on the name of our Lord Jesus Christ, both their Lord and ours (1 Corinthians 1:1-2)
Paul, an apostle of Christ Jesus by the will of God, and Timothy our brother. To the church of God which is at Corinth, with all the saints who are in the whole of Achaia (2 Corinthians 1:1).
According to the Acts, we can chart Paul's itinerary as follow:

1. Paul left Athens and arrived at Corinth (Acts 18:1).
2. He worked there with Aquila, Priscilla, Timothy and Silas for 18 months. The Jews in Corinth united to attack Paul before the proconsul Gallio who threw the case out of the court. The Jews seized Sosthenes, the ruler of the synagogue, and beat him up in front of the tribunal. The proconsul ignored them (Acts 18:17). So, we have Sosthenes.
3. Acts did not mention Sosthenes anymore. He was beaten up in Corinth and might have been deposed of the role as the ruler of the synagogue. Probably, he continued to stay with the Christian community in Corinth. But all these are conjectures. 
4. After this incident, Paul took Aquila and Priscilla and sailed for Syria. Probably, Paul left Timothy behind in Corinth to take care of the community. On the way to Syria, Paul reached Ephesus (Acts 18:19). He did not stay long and travelled all the way back to Antioch (Acts 18:22).
5. Then he travelled by land in the north, Galatia and Phrygia (Acts 18:23) and finally returned to Ephesus (Acts 19:1).
6. Paul worked there for three years. Probably, Aquila and Priscilla were among Paul's co-workers in Ephesus. Their names were not mentioned but Paul continued to work as a tent-maker. We are able to identify Timothy and Erastus when Acts mentions that Paul sent them to Macedonia, which is north-west of Ephesus, while he himself stayed for a while in Asia (Acts 19:22). Somehow, Timothy had followed Paul to Ephesus and worked together.
   Within these three years, did Paul visit Corinth?
7. Then a riot instigated by Demetrius the silversmith, occurred in Ephesus because of the success of Paul's missionary work (Acts 19:23-41).
8. After the riot, Paul went from Ephesus to Macedonia to rejoin Timothy (Acts 20:1). A whole group of people went down to Troas first (Acts 20:5).
   Paul picked Luke up in Philippi to join the bunch. Would it be possible for Paul to pay a visit to Corinth on the way to Philippi?
9. In Mitylene, Paul assembled the elders from Ephesus and delivered his farewell speech (Acts 20:18-38).
10. Then Paul returned to Jerusalem and was arrested there (Acts 21:17-40).

When Paul mentioned Sosthenes and Timothy in his epistles, can we assume that they were staying with Paul? Hard to tell. Had Sosthenes and Timothy been in Corinth, they would have been the recipients rather than the co-senders of those epistles. But this argument only shows that Sosthenes and Timothy were not in Corinth and can hardly prove that they were staying with Paul in Ephesus. Scholars agreed that the epistles were written in Ephesus. Therefore, we may assume that Sosthenes and Timothy were also in Ephesus when Paul wrote the epistles to continue the discussion.
The First epistle mentions Sosthenes instead of Timothy. We may assume that this epistle was written in Timothy's absence. In point #6 above, Timothy was sent to Macedonia. It was very likely that Paul wrote this epistle after sending Timothy to Macedonia.
The Second epistle mentions Timothy instead of Sosthenes. Applying the same logic, Sosthenes might NOT have arrived in Ephesus yet. But there was another possibility. Sosthenes had NOT yet reached the same status as Timothy in the church work. Whichever the possibility, the Second epistle might be written before the First!
The whole discussion might be overturned by a verse in the Second epistle.
For we do not want you to be ignorant, brethren, of the affliction we experienced in Asia; for we were so utterly, unbearably crushed that we despaired of life itself (2 Corinthians 1:8).
What would this affliction be? Does it refer to the riot in Ephesus mentioned in point #7 above? But Timothy was in Macedonia when the riot happened. Therefore, it is also possible that Paul wrote this epistle in Macedonia rather than in Ephesus!
Of course, this is just an exercise for the sake of curiosity. It is not rigourous enough to overturn the accepted wisdom of scholars. Indeed, some scholars draw our attention to the "temperature of the relationship" Paul had with the Corinthians. The two epistles show swings of this relationship. This is legitimately a more powerful analytic tool that just the names of the co-senders. Such an analysis would only be done much latter.

Dear Lord, John Tang was cremated this morning. I can still remember his rough and forceful pair of hands. May his soul find eternal repose in You. Dear Mr. Tang, pray for me before the Lord so that this unworthy servant may serve our Lord well. Amen.