It's been said a few times in this thread that CFIs have superpowers when it comes to loggings. That is where I was getting concerned. As a CFI I have alway been under the impression that if I am on a cross country with a student i can log it as such. I haven't been able to find any opinions that support that claim. Reading through those three left me with a sense of No you can not log it unless you do the landing.
You're over-analyzing.
First, back up to the beginning of 61.51(a)(1)(2)&(b) without quoting word for word, says how to log to show experience requirements for ratings and/or currency.
You're not logging x/c for a rating, are you? If you are for ATP, then you don't have to make a landing.
The 61.51 rules are for pilots getting ratings, or meeting currency.
As a CFI, you don't even have to meet currency to fly with a student.
As a CFI, log in accordance with 61.51(e)(3)
You, and others, are not seeing 61.51(e)(1) starts with "A Sport, Recreational, private, or commercial
pilot may log..."
If you are instructing, log as an instructor.