Some experts will be along presently, I expect, and give you an authoritative answer. From memory I seem to remember that jbtsax likes to polish the inside of saxes when he repairs them and that it makes a noticeable difference.
The higher up the sax, the more effect little differences have on tone (like mp and oral cavity!) so the inside of the crook is worth keeping clean. I always wash out mp and crook with clean water after playing and thoroughly dry inside and out with a soft cloth, and once in a while a skinny bottle brush with a little detergent in the water, followed by water without detergent.
I see Stephen Howard recommends filling the neck with vinegar for at least half an hour if really dirty and encrusted, protecting the octave pad with clingfilm or Bluetack and bunging up the top end, then rinsing with water thoroughly afterwards.
Apart from swabbing through after playing - I use a homemade pull-through, half a wine cork, a thumbtack to secure a length of light line and a soft cloth secured with a swab hitch - it is risky to attempt cleaning the inside of the body, although S.H. suggests a pipe cleaner is worth using to clean inside the octave key tube once in a while (same on the neck).
I wouldn't think that lacquer on the inside of the bell would make any difference. Unless the other two saxes are really grotty inside, especially nearer the top end (octave key tubes?) I would have thought that the difference you mention is more likely due to other things.
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