Let me share one possible way:
Say you're out in the ministry with another asleep JW and it's your turn to speak to the householder. You can steer the conversation in such a way that you can talk about the pharisees' unreasonable interpretation of the sabbath law and how it was contrary to what God intended. You work your way to the point of saying:
"So you see, even though the law said that the Israelites were to abstain from work on the sabbath, that didn't mean they were to let someone die from lack of lifesaving assistance or healing work as performed by Jesus, just because it's the sabbath. Likewise, even though all the regular israelites were to abstain from eating the show bread in the temple, David and his men were mercifully exempted from condemnation when they took the show bread to save their life due to their hunger. Jehovah is a reasonable God and does not intend for obeying the letter of the law to result in needless death or suffering in extenuating circumstances. That was the point Jesus was emphasizing when he said 'I want mercy and not sacrifice'"
The words that I bolded are what I consider key words that are commonly used when discussing the no blood doctrine. Using them in the manner quoted above could trigger the mind of your asleep JW partner to start thinking about the no blood doctrine and see the parallel.
I would love to hear your ideas on how TTATT can be shared subliminally.