That was white ringneck called Jeff, i would not phase out the nebuliser but just use water with no addatives. the fact that your bird still gets wheezy shows that he still needs the calming mouster that the nebuliser brings. i would not use a blanket over the cage now and allow the steam to raise up to yor bird, he then will not see it as a punnisment and start to enjoy it more and being able to avoid some of the steam it will still make the air around him moist. One thing a did not mention is his dry food shold be removed when steeming. try this and let me know how he gets on