A very good topic, Lady Liberty!
Obviously, if God permitted Jews to sell an unbled carcass to non-Jews for consumption, then he was giving explicit permission for non-Jews to eat unbled meat. Therefore, if God is consistent, then his words in Genesis 9 about not eating "flesh with its soul -- its blood" cannot apply to animals found already dead. Therefore the prohibition in Genesis 9, supposedly to all mankind, can only apply to animals specifically killed for food, and the reason is simply to respect the giver of life when one takes an animal's life for food. That's really all there is to it.
The Watchtower Society, though, cannot accept this obvious fact, because of its tradition since about 1945 that blood transfusions are wrong based on Genesis 9. Its leaders know perfectly well that abandoning this ridiculous doctrine would not only lose them a lot of followers, but a lot of money in the form of contributions and, especially, lawsuits. They would also have to admit gross bloodguilt. If they admitted this, then of course the entire "faithful and discreet slave" doctrine would collapse.
Watchtower leaders are well aware of the scriptural problem, but cowards as they are, they won't discuss the issue in print. However, several years ago, shortly after I learned about this argument based on Deuteronomy 14:21, I called one Fred Rusk, who for many years has been one of the key WTS officials responsible for doctrine on blood. After I explained the issue (he was already familiar with it) he admitted that God indeed gave permission for non-Jews to eat blood, but that he did so only because of their "hard heartedness". He claimed that it's a situation similar to the way Jesus said that God had permitted Jews to divorce their wives because of their hard heartedness. Well of course this is pure special pleading, and there is not a shred of evidence to support Rusk's claim. The only reason for such a claim -- and this is the special pleading -- is that it's needed to get around the obvious logic as I explained above. And of course, JWs who hear an explanation like Rusk's from the Society will automatically accept it since it's coming from "the slave", who speaks for God. Obviously, with this kind of "reasoning" JWs can justify anything they like -- and they do! So this is yet another example of the house of cards doctrines that are the foundation of JW belief. In order to keep their belief in WTS leaders as God's spokesmen, the lot of them are forced to be intellectually dishonest.
AlanF