You are to be commended for the good job you are doing to try to attenuate the effects of cat dander. Two things to note: 1) the allergy cover on your mattress and box spring can limit your exposure to house dust mite, but not to cat dander, especially if your cat is allowed to come into your bedroom, and 2) if at all possible, you should arrange for someone else to do the vacuuming when you are not present and will not be present for 3 to 4 hours after the vacuuming.
To answer your questions: There is no guarantee that the nasal washes will provide an adequate sinus rinse. What you describe as “huge blogs of mucous” might be comprised of a fungus that is causing a condition called, allergic fungal sinusitis. The color is consistent with infection, either bacterial or fungal. You should ask your doctor to send some of these “blogs” to the laboratory for fungus culture and microscopic examination. Why you get blogs out only some of the time is due to variations over-time, of sinus mucus clearance and has no other significance.
Good luck.
forgot to add ...
I tested positive for cat and dust mite allergies.
I do have 2 cats in my house that are now getting bathed once a week (plain water) and using allerpet-c to denature the dander protein. Plus I have an allergy cover on mattress, box spring and pillow that is suppose to stop cat dander as well. And vacuuming with a hepa filter once a week.