Maybe it's an older one.
I was thinking about it and I think one of these books was really old, perhaps pre-WWII.
That would make more sense because that's when blood transfusions were first becoming widespread.
Believe me, I KNOW John R. Rice's more interesting doctrinal digressions, and this was NOT one of them!! In editing his book of sermon illustrations, I read or skimmed every single one of his 200 plus books and pamphlets, and he said nothing about blood transfusions. This is actually a JW doctrine, and I've never heard of it anywhere else!
I would be extremely surprised John R. Rice wrote this in a book anytime. The truth is, John R. Rice wrote very few books before WW2. He started the SOTL as a newspaper in 1934, and didn't really hit his stride as an author and publisher until the early 1940's.
Books he wrote before WW2 can be counted on one hand, and I have read and/or own all of them: Bible Facts About Heaven (his best seller, with over 500,000 in print, originally published by Moody Press), What Is Wrong With the Movies (1938), a book of the famous Rice/Oliphat (a Church of Christ preacher) debate and a couple of others.
When I worked at the Sword of the Lord I often looked at the shelves where they had every book John R. Rice had ever written. Believe me, I would have known if he had taken this position. He never did.