Non-pilot speaking.
You say, "the time taken for us to fly through it's contrails" but did you mean to say, "the time taken for us to fly ACROSS it's contrails". In other words, OVER and ABOVE them?
There are many such questions in various forums in PPRuNe (probably one a month) and the professionals usually say that it is very difficult, even for a pro, to accurately judge height - whether the observer is on the ground or in another a/c.