Welcome to photrio.
I make salt prints, not albumen, so I don't have direct experience with this and I'm guessing a little here. I have made quite a few salt prints on this paper ( it has a nice bone-white color and a nice "pebbly texture"... very good for some prints! ), and I have seen black spots and other problems appear during the final wash with other papers -- it's common ( and frustrating! ) for problems to pop up at the end like that. I have not seen black spots with Canson Universal Sketch, which is probably a good thing, since I always wash my prints for at least an hour and usually 2 hours -- it makes me think your black spot problem might have a solution. When problems appear in the final wash or as the print dries, it's usually because the moisture has reached deep into the paper, under the sizing ( or albumen ) and something has reacted with the internal sizing or the internal alkali buffer ( this paper does have an alkali buffer ).
I can't tell how big your print is, but here's what I'd do. Make some small test prints ( like 5x7 inches -- to save on cost of silver nitrate ), and try extending the first wash before you fix the print. Start with plain water and change it at least 3 or 4 times, keep changing the water until you can not see any cloudiness come off the print any more. Then let the print soak in clean water for 10 minutes, twice. Then wash for 3 minutes in water with a few shakes of salt in it ( a teaspoon per liter is fine ). Then rinse several times and soak for 3 more minutes to wash out the salt water. Only after this long washing, then fix the print in hypo ( and, given your problems, you might fix for longer than before, and using at least 2 separate baths of hypo. ) Finally, a long wash, at least an hour, changing the water every 10 minutes or so.
If the black spots don't happen on your test print, then you've got it figured out. If they still happen, there are some other things you can try. Photrio member Herzeleid has posted instructions for using strong ammonium chloride solution in the wash sequence. I've tried it and it worked very well for me, and it is probably a great thing to try if you are still having problems. Another possibility would be to acidify the paper before you coat the albumen, and/or add a little citric acid to your silver nitrate. But I think you should try extending the 1st wash first, before going to something more complicated. I will go and find Herzeleid's instructions and post a link to them here in this thread.
Make sure there's no chance of any metal contamination ( like an iron pot, or a rusty wire whisk to foam the albumen ) anywhere in your process! That's a well known cause of black spots in salt or albumen prints.
Good luck and have fun.