Edit 2: Figured out how to set hotkeys for inventory items. It turns out the new UI area of the editor does not allow you to modify the gamestrings.txt and gamehotkeys.txt file. For anyone else interested, you need to use an MPQ editor and open up your <map name>.SC2Map file. Then browse to <map name>.SC2Map/enUS.SC2Data/LocalizedData and edit the GameHotkeys.txt file. Remember to exit the SC2 editor and game first so that you can edit the files.
For example, I added the following lines to GameHotkeys.txt:
The above lines specify hotkey aliases that I can now use in my custom UI files.
So now that I've saved the updated GameHotkeys.txt file, I re-open the editor, go to the UI section, find the button that I want to add the hotkey for (in this example I had first created an override file to change the UI layout of inventory container buttons), and add the appropriate <Shortcut> tag line:
<Frame type="CommandButton" name="Slot01">
<Anchor side="Left" relative="$parent" pos="Min" offset="0"/>
This sets the first inventory slot to have '1' as its hotkey (as specified in the GameHotkeys.txt file)