Well, I've had a bit of a rummage around, and like your extracted pictures above, I'm not sure that anything is any more clear...
The first challenge that I had was finding some reference. Googling for images of North Sunderland coaches seemed to give lots of pictures of four-wheel coaches, but it was difficult to get clear picture of any six-wheelers.
I then went back to searching the indices and contents of the Great Eastern Society Journals. As the society covers the successors to the GER, then I hoped that there may be something covering LNER or BR(E) usage of the coaches. Sadly, the only references to Sunderland were in football matches against Arsenal, and the so-named B17 and Class 66 locomotives...
Also in a couple of issues of the GEJ are a history by John Watling of GER coaching stock, summarising the development and design. I found that this is also on the GERS website at https://www.gersociety.org.uk/index.php/rolling-stock/carriages/introduction
. Unfortunately, due to the convoluted way that the GERS holds rights to many images in their collection, the (more helpful) photographs of coaches included in the article have been replaced by line weight diagrams. The articles themselves also focus on the design "above solebar" and make virtually no mention of the underpinnings.
I do have the copies of the print magazines that this article is in, with the original pictures. Even given the exceptionally clear definition on some of the pictures, I still can't find a clear picture showing any safety loops. I don't have any construction diagrams of GER coaches - it's not really my interest, which is more on the goods stock - either, so I'm afraid that I don't have that as a way forward.
So in conclusion, in the absence of any positive confirmation of visible safety loops, I think that you would be on safe ground leaving them off. Until that elusive photo showing them turns up!