Good deal on Beaker Boy's weight gain, that definitely means he is getting better. Have you thought of maybe putting a humidifier in the room at night where Beaker sleeps? During winter times, atleast here in AR the air in the house is so darn dry. We use one and it really helps add moisture to the air. We don't feel like we wake up with that dry cotton mouth feeling anymore...or coughing
We used it also with a pup we had a few years ago (returned it to the breeder) was congestion and such. We added Vicks to the water and it helped tremendously.
Regarding the bathing? Schatzie doesn't have any skin problems but she is bathed every 3 days. Her hair seems almost human like and she looks rather gross if I don't bathe her that often. That is even with daily brushings, etc. Gosh, If I had to wait 3-4 weeks to bathe her i don't think Id be able to recognize her.

But your vet might be telling you that because of Beaker's sensitive skin.
I hope Beaker's cough goes away soon and continue's getting better. Thanks for giving us an update on him.