I agree with CarolynnM to a point. I certainly agree that we can only speculate!
But in that situation, I would certainly have promoted changing positions til we found one that helped at least a little. Side-lying, H&K, upright--any of these may have helped at least a little. If birth is rapid, it doesn't matter as much--but still, a woman can roll pretty quick to sidelying.
But I'm a little confused here--in your thread title, you say 'cord compression', but in your post you mention 'releasing the tension on the cord'. THis is two different things as I see it--compression being the squeezing of the cord, by being caught between baby and pelvis as baby descends. Not sure how you meant it, but seeing the word 'tension on the cord' makes me image a cord pulled tight (around the neck in particular).
If the cord was pulling tight, I tend to agree more with CarolynnM...I don't konw as there is anything to be done about that. If it was more about compression, then position change may well have brought *some* relief. However, having seen a few well-wrapped babies like the one you describe, I think there is just no avoiding a degree of cord compression--again, you might affect some relief, but probably not total relief from compression.