There's no flaw in your logic. You're spot on.
There may even be additional flaws in the JW logic you haven't realized yet.
Here are two:
1. The phrase "Abstain from blood" is not grammatically complete. You cannot invoke a partial predicate apart from the context that completes it as an independent construction.
For example, what would it mean if someone were to come up to you and out of the blue, say, "Abstain from car" ? You can abstain from driving a car or riding in a car, or washing a car, but the idea of an abstinance from the car itself is meaningless. This is because technically we don't actually abstain from physical objects, we abstain from finite acts done in connection with these objects. Therefore a finite verb is needed to complete the thought. When the verb is not present, the reader picks it up from the context. --If someone were to say, "Abstain from liquor" you would automatically know that they were talking about drinking it.
The same is true of blood. In context, the phrase, "Abstain from blood" is a reference to eating it. Many translations render the phrase as, "Abstain from eating blood" or something to that effect. (e.g. Moffat, Today's English Version, Contemporary English Version, New Life Version etc.) Transfusion is not eating blood. It is a form of organ transplant.
The JW invocation of the phrase "Abstain from blood" is just a cheap, ungrammatical trick to try to force a comment out of the Bible that it never actually makes.
2. There is no Biblical requirement to pour all blood out on the ground.
Ancient people would kill a domestic animal that they intended to eat by quickly slitting its throat with a very sharp knife. Wild animals don't let you walk up to them and slit their throats. Wild animals don't usually even let you get near them. Methods for killing a wild animal (e.g. A spear, arrow, snare, etc.) do not sufficiently bleed the carcass. Therefore under the Law, when a wild animal was killed, additional steps were necessary. The throat still needed to be slit and the blood poured out even though the animal was already dead.
With these facts in mind, read the scriptures the JW's use to substantiate their idea that all blood must be poured out on the ground. You will see that they are contextually specific instructions to Israelite hunters about what to do with a stag, hart, gazelle, and wild fowel after you have killed it.
Blood needed to be removed from the body by being poured out.
The JW's have taken that requirement, divorced it from the original context (Hunting) and reworded it into this:
"Blood removed from the body must be poured out."
However that's not what the Bible says and this is just another cheap trick to try to force a statement out of the Bible that it never makes.