Is there a way to have a transaction filter the available items based on the Department selected on the Transaction? We’d only want items for that department (and its subdepts) to show as options to be added.

Not natively as far as I know, is it possible to implement a custom column to be used when adding items and hide or restrict the native item column.

You could setup a custom form for each department and then use the saved search filter on the form to filter to only specific departments...however, depending on the number of departments that would get tedious and annoyting to manage. Plus the workflow isn't great if people have to select different forms based on dept. The only other alternative I've seen is like @alien4u described. Setup a custom column field with filtering via client script then use that custom field to source your native Item field. You can also do this via after field edit action on a workflow but a script has more control over other things that need to populate.