Is it possible to have a multi-line text entry field with drop down options?
I currently have a GUI with a multi-line Text widget where the user writes some comments, but I would like to have some pre-set options for these comments that the user can hit a drop-down button to select from.
As far as I can tell, the Combobox widget does not allow changing the height of the text-entry field, so it is effectively limited to one line (expanding the width arbitrarily is not an option). Therefore, what I think I need to do is sub-class the Text widget and somehow add functionality for a drop down to show these (potentially truncated) pre-set options. 
I foresee a number of challenges with this route, and wanted to make sure I'm not missing anything obvious with the existing built-in widgets that could do what I need.
I don't think you are missing anything.  Note that ttk.Combobox is a composite widget. It subclasses ttk.Entry and has ttk.Listbox attached.
To make multiline equivalent, subclass Text. as you suggested.  Perhaps call it ComboText.  Attach either a frame with multiple read-only Texts, or a Text with multiple entries, each with a separate tag.  Pick a method to open the combotext and methods to close it, with or without copying a selection into the main text.  Write up an initial doc describing how to operate the thing.
Multi-Line Combobox in Tkinter