There is actually a simple solution that, of course, gets overlooked by the Jehovah’s Witnesses. Acknowledging that there are still debates and other workable (albeit complicated) solutions to this problem, the simplest answer is often the most overlooked:
Acts 15 is an edict designed to preserve Jewish practice among Judeo-Christians while acknowledging that Gentiles are not to be bound by the same in Christ. Jehovah’s Witnesses view Acts 15 as a historical change for all Christians, a point in time when Christianity began to pull away from Jewish practice. This is not the case. Acts 15 merely reiterates part of the Jewish Tradition, namely that Gentiles are under the Sheva Mitsvot Bne Noah or the Noahide Laws, and that their introduction into the Body of Christ (the foundations of which are Jewish) does not change this. As such, Acts 15 neither introduces anything new (as Jews have always viewed Gentiles bound by Noahide Laws), and as Acts 21.15-26 proves, neither does it introduce a change for Jewish Christians.
1 Corinthians is telling Gentile Christians how to apply (and perhaps even introducing them to) Sheva Mitsvot Bne Noah. Most ancient cultures, including that of the Jews, butchered animals for daily eating as part of a religious ritual. Animals were slaughtered and their blood (or spirit) was offered back to the deity worshipped by the butcher (or priest), and eating the remaining meat was seen as a type of “communion” with the deity. Since the only practical way to get meat to eat was through the market run almost exclusively by pagans who butchered their meat this way, Paul taught the Gentile Christians that since they were not actually taking part in the sacrificial act and worship, their eating of the meat was not partaking in communion to idol gods.
Especially if we were Jehovah’s Witnesses, we were likely taught (or took it for granted) that the Jews sacrificed animals merely to have sins forgiven and that God introduced this “system of atonement” for their sins in the Tabernacle/Temple arrangement. But Jehovah’s Witnesses could not be more wrong.
Practically all the ancient cultures believed that their deities allowed them to eat the flesh of animals as long as they thanked their gods for the life of the beast by ceremonially pouring out its blood. The ancients viewed blood as sacred because they believed that the “life force” or the “soul” of a creature was actually in its blood and had thus had the power that made up life (which they also believed about seminal fluid and the blood of menstruation flow). These bodily fluids were thus treated and offered to deities in very special ways.
This ancient, almost universal belief or understanding is what is being spoken of here in both Acts and 1 Corinthians. If you offer the blood of an animal (or any other part of it) in a butcher/priest system in which the butcher makes the offering to an idol, are you then (by eating the meat )having religious communion with the false god? Paul answers “no.”
In the Greco-Roman world, meat sellers butchered their animals in the marketplace, offering the blood (and sometimes things like the fat and entrails) to whatever deity they worshipped. Not to do so was considered blasphemous in the heathen world, a dishonor to the gods and to the society you sold your meat to. There was no other meat to buy in the Gentile world (unless you went to Jerusalem and ate kosher meat properly slaughtered by regulation of the Mosaic Law at the Temple--or did it yourself). The Gentile world of the time was just as cosmopolitan as the Western world of today, and most people did not raise their own livestock for meat. You want meat? The marketplace was the only way to get it. And who butchered the meat? Jewish priests? Nope, these were heathen or pagan butchers.
And that is all this is. Again, Acts 15 introduces nothing new, merely preserving Jewish custom while upholding the teaching that Gentiles are only bound to observe the Noahide Laws (which included refraining from idolatry and the active participation in communion to idol gods), and 1 Corinthians is Paul explaining to Gentile Christians how to apply these laws in their particular circumstances.