1 Corinthians 15.5-54 and 1 Thess 4.13-18 are commonly used to interpret each other:
1 Thess 4.13 But we do not want you to be uninformed, brothers and sisters, about those who have died, so that you may not grieve as others do who have no hope. 14 For since we believe that Jesus died and rose again, even so, through Jesus, God will bring with him those who have died. 15 For this we declare to you by the word of the Lord, that we who are alive, who are left until the coming of the Lord, will by no means precede those who have died. 16 For the Lord himself, with a cry of command, with the archangel’s call and with the sound of God’s trumpet, will descend from heaven, and the dead in Christ will rise first. 17 Then we who are alive, who are left, will be caught up in the clouds together with them to meet the Lord in the air; and so we will be with the Lord forever. 18 Therefore encourage one another with these words.
On the reading of 1 Cor 15 that I favor, which is a common one but not incontestable, Paul is quite aware of the problem of decomposition that you bring up and that is why he introduces the concept of spiritual bodies. The Greek ἀνάστασις νεκρῶν is usually translated into English as 'resurrection of the dead' but might be more literally rendered as 'standing up of corpses". This is a specifically Jewish idea that probably would have sounded very odd to Paul's Corinthian audience, which was probably predominantly Gentile. As Greek speakers living in Greece, they likely understood the concept of the immortality of the soul, which goes back at least as fas as Plato some four centuries earlier. But the Jewish concept of corpses getting up out of their graves on resurrection day probably sounded very odd to them.
Paul engages in some clever rhetoric to persuade them. First, they have already accepted that Jesus rose bodily, so they know this is possible (1 Cor 15.12 ff). Paul is arguing that Jesus's resurrection was the first, but the other resurrections will be of similar character. Second, the Corinthians are thinking of physical bodies of flesh, which are not what will be raised (that would indeed be silly), but bodies transformed into spirit or spiritual bodies such as God will give them. Paul is blurring the categories in which the Corinthians thought. If they believe in the immortality of the spirit, how can they object to spiritual bodies? This probably made the Corinthians scratch their heads a bit as the word πνεύμα, which means spirit in this context, but is also the word for wind and breath, and has the connotation of insubstantiality. So the dead, according to Paul, will have a form, but it will be a form made of spirit. The risen bodies won't be rotting corpses but transformed bodies made of spirit, so Paul's seems to be trying to make the Jewish belief in a bodily resurrection compatible with the Greek belief in the immortality of the soul or spirit. Yes, people will be resurrected with bodies, but they'll be transformed bodies made of spirit.
Best,
Ken
PS Yes, I take 1 Cor 15 to be authentic
PPS When I re-read the question, I realized I didn't answer the part about whether the natural or earthly bodies remained where they were buried when the dead received new spiritual bodies. I think the answer from the later church would be no (hence the empt tomb story in Mark). But what Paul would have thought is indeed a good question. (And I realize my use of the term 'the dead' there is problematic. It's not really clear what it is that's continuous between the former earthly person who died and the transformed spiritual person who was raised - that's the issue).
