Old Kodabromide? Easy answers to your questions...
1. Age. Kodabromide ceased to be produced - when? 30 years ago? Even frozen, it would be way past their prime now. In fact, unopened boxes of the stuff fetch more (as collectibles) on THAT web site than more recent stocks of Kodabrome RC. Believe me. I have sold some before, so I know!
2. It was a quite fast paper, in its day. The three last words are the clincher. You are trying to print with antique paper.
3. Not sure how you did your tests, so cannot comment. In my experience, unexposed paper doesn't readily show fog. Make a print on it, and you will see how it turns out. If mostly grey, it's gone.
Here is someone who, just last month, disposed (profitably, I must say) of 2,500+ sheets of Kodabromide/Kodabrome I had lovingly kept deep frozen for the better part of - hm. Since 1990-1991, I think. Did some basic tests, and found it unusable.
There comes a time in the life of every darkroom worker, where the bullet must be bitten, and one must accept that some papers (and films) are just too old to be useable. Again, I know of what I speak. Am just now waiting for 100 rolls of Kodak Panatomic, frozen about 1987-1988 when, if memory serves me reliably, Kodak ceased to produce it. Three 100-foot bulk rolls, the rest 36 exposure pre spooled rolls. I will test shoot 1-2 of the rolls, and if it still produces images, then I may list the rest for sale, if it is useable. Believe collectors pay ridiculous prices for it. I went to the Tmax films in the 1990s, and when I had worked out how to process that then somewhat fussy emulsion correctly, have never looked back.
So why did I keep the frozen stocks so long? Hm. Why do I still insist on doing photography with a Nikkormat and a Rolleiflex?
You and I may be kith and kin...