A few copies show on the secondhand listings. I find, for example

Jack Downing's Song Book: Containing a Selection of About Two Hundred Songs, Many of Which are New. (Providence: Weeden and Cory, 1835, 32mo. pp256, 1st edn).

Jack Downing's Song Book. Containing A Selection Of Upwards Of Two Hundred Of The Most Popular Songs, Many Of Which Are New. (Providence: B. Cranston & Co, 1839, 5th edn).

Not too many references online, though one indicates that Scott's Harper's Song was included.

If you'd like to post a list of the contents here, that would be interesting; and we may be able to help with some of those you haven't placed yet. In those cases, perhaps adding the first few lines would help, and prevent wild guesses based on vague similarities of title.

Can't say I've anything useful to add on that Mistletoe Tree at the moment, but something may well come up. There are an awful lot of songs that were widely printed in songsters of the day which are quite forgotten now.