You will realize that in Acts 20:7 the meeting and breaking of bread was done in the night, meaning, or if we may presume, that these people had been worshiping together on the Sabbath. Since we know that a day then started at sunset, so Paul did preach to them. just as we Christians do today when we fellowship of Wednesday or Friday nights.
"Now on the first day of the week, when the disciples came together to break bread, Paul, ready to depart the next day, spoke to them and continued his message until midnight" (Acts 20:7).
You seem to be aware that during the days of the New Testament, two different time systems were in use. The Jewish style of keeping time was to mark a day from sundown to sundown (roughly 6 pm each evening). The Roman style was the same as we use today, marking a day from midnight to midnight. The problem is that you play fast and loose with which time system you are applying to the text.
First, there is no need to presume anything. The text clearly states that it was the first day of the week. If you use the Jewish time system, then it means they meet after sundown on what we call Saturday, but what the Jews call the beginning of the first day of the week. If the Roman system of time was being used, then the meeting took place on what we call Sunday. In either case, it remains the first day of the week. It should be noted that Troas is a Gentile city, it is not even close to the borders of Israel. The time system they most likely used was the Roman system.
It also states that the first day of the week was the time when the disciples came together to break bread. You try to relegate this passage to a simple, informal gathering, but two things interfere. First, the wording states that there was a regular meeting by the disciples on the first day of the week. Second, this regular meeting was for the purpose of breaking bread.
The phrase "break bread" is term for eating a meal. It can apply to a common meal, such as "So continuing daily with one accord in the temple, and breaking bread from house to house, they ate their food with gladness and simplicity of heart" (Acts 2:46). We know that it was a common meal because it said they ate their food and that it was done from house to house, not in a single gathering. Breaking of bread can also refer to the Lord's Supper, the fellowship meal of which all Christians partake. "And they continued steadfastly in the apostles' doctrine and fellowship, in the breaking of bread, and in prayers" (Acts 2:42). Though in the same chapter, we know this reference was to the Lord's Supper because it was connected with other aspects of worship. The clearest reference is, "The cup of blessing which we bless, is it not the communion of the blood of Christ? The bread which we break, is it not the communion of the body of Christ?" (I Corinthians 10:16).
So which one was being addressed in Acts 20:7? A common meal, or the Lord's Supper. The key is that we find that they were coming together regularly for this breaking of bread. "For first of all, when you come together as a church" (I Corinthians 11:18). Paul then goes on in I Corinthians 11 to both scold the Corinthians for their abuse of the Lord's Supper and to give instructions on how the Lord's Supper is to be observed. A bit later, in giving instructions for how worship services are to be conducted Paul states, "Therefore if the whole church comes together in one place" (I Corinthians 14:23). The combination of "coming together" for the purpose of "breaking bread" tells us that the disciples in Troas gathered on the first day of the week to partake of the Lord's Supper -- thus they had come together for worship and not just a study with Paul as you asserted.
We don't know when the service started, but we do know that it went past midnight. Thus by either Jewish or Roman measurement we know the gathering extended that day into the second day of the week. It was about midnight that Eutychus fell from the window and was restored. Paul then returned, ate a common meal, talked until morning and left at dawn (Acts 20:11).