This variety of Klebsiella Oxytoca is an uncommon cause of disease and found primarily in the intestine. That it would be cultured from the nose and/or sinuses raises the question of an immunodeficiency disorder. The question to be answered is, Is this just colonization, the cause of the thick mucous or is it actually an invasive infection. If what you have is just colonization, it might not be necessary to eradicate the Klebsiella and, as this organism is typically resistant to multiple antibiotics, perhaps impossible.
Should it not be possible to eliminate the blockage, surgically or otherwise, the provision of supplemental oxygen via the mouth or directly into the trachea, might allow for the effective use of oxygen.
My advice is that you be tested for immunodeficiency and that you request consultation with an Infectious Disease specialist. With the exception of antibiotic eradication of infection, there is no effective way to alter the physical characteristics (thick) of mucous.
Good luck
Thank you for your input doctor Tinkelman, intend to follow your advice.