With regards to your interpretation of Matthew 24: 34-41, you should have continued on to Matthew 24:42-44 which makes it clear who is being taken and by whom:

42 “Therefore keep watch, because you do not know on what day your Lord will come. 43 But understand this: If the owner of the house had known at what time of night the thief was coming, he would have kept watch and would not have let his house be broken into. 44 So you also must be ready, because the Son of Man will come at an hour when you do not expect him.

Who is the Thief in this passage? The Son of Man (Jesus Christ). Who is He coming for? His possession, the bride or the church, who is betrothed to Him.

You can speculate all you like about what the taking or being left is all about, but you can't superimpose the flood onto the rapture because they are different events. The one thing they have in common is that God will save those whom He has chosen BEFORE the judgement event, and that is also in common with the Sodom and Gomorrah judgment. In both cases, those chosen to be saved left the scene of judgement beforehand, having been warned that the judgement was coming. In Noah's case, he had to build a boat first, in the case of Abraham and Lot, they just had to leave the city before the fire and brimstone fell.

The other question I would have for you, is why would the Roman Armies take away those who have not put their faith in Christ? Surely in that kind of scenario it is the Christians who would be persecuted as they were in the days of the Roman empire. So no, I don't agree with your analysis of the left behind passage in Matthew 24. Plus there are other scriptures which clearly teach that there is a rapture.

1 Thessalonians 4:
15 According to the Lord’s word, we tell you that we who are still alive, who are left until the coming of the Lord, will certainly not precede those who have fallen asleep. 16 For the Lord himself will come down from heaven, with a loud command, with the voice of the archangel and with the trumpet call of God, and the dead in Christ will rise first. 17 After that, we who are still alive and are left will be caught up together with them in the clouds to meet the Lord in the air. And so we will be with the Lord forever. 18 Therefore encourage one another with these words.