All of this quoting of scriptural verses written thousands of years ago shows the care that needs to be taken when applying old "rules" to the modern-day setting. It is fraught with danger and the results of literal interpretations are often tragic.
The Bible says taking blood in an emergecy is O.K 1Sam 14:24-46 and more!!
Side point (to this thread, not to the text it invokes as prooftext): in 1 Samuel 14:32ff "eating along with the blood" is a common (already LXX, sun tô haimati)but dubious translation of the rare Hebrew idiom, 'kl `l h-dm, literally, "eating over the blood" (also Leviticus 19:26 and Ezekiel 33:25).
Most likely this phrase originally referred, not to eating unbled meat, but to a specific religious / divinatory practice (rejected by the later official Judaism which produced the texts) of eating the flesh of an animal on the very spot where it had been killed (probably because such ritual sharing would allow for communication with the underworld). Maybe it implied blood eating, but that's uncertain and definitely not the main point.
Even if this earlier meaning is partly lost in the later rewritings of the Hebrew narrative in 1 Samuel, it is still apparent imo: the animals had been slaughtered, shcht, hence bled (btw it was certainly the quickest manner of killing cattle) onto the earth (vs. 32). And Saul's response is to move the place (not the way) of killing to a "rock," i.e. an ad hoc but approved altar to Yhwh (v. 33-35; we're still in the perspective, different from Deuteronomy, that every killing is a sacrifice).