Found another recording of "Everything Is Hotsy-Totsy Now" here, an unreleased test pressing by Irving Mills (who co-wrote the song) and Duke Ellington. I was able to decipher a fair bit of it, but I'm not sure of a few lines; see the italicized bits below.

Intro:
...A cozy little home,
Just room enough for two-two-two.
There's a hope to add a limb on the family tree.
(Could be "There I'm gonna"--another singer sings just "Gonna". It sounds to me most like "There's a room" but I'd be surprised if that were it.)

2nd refrain:
So long, sadness; hello, gladness,
Roll up to my bow
(Maybe "Row up"? The "bow" bit is rhyme-paired with "now".)

3rd verse:
...And when we spoon, she don't play copsy,
She don't call momsy or her popsy.
(Possibly "play copsy" should be "say stopsy")

3rd refrain:
Say I've loved others,
So, old brothers,
??? with a smile.
I'm sure glad she
Found out and she's happy
She's glad meanwhile.

Any help appreciated.