Hello Dan,
From my (albeit very limited) knowledge of Finale, I don't think it would easily be able to edit MIDI files recorded by Hauptwerk's built-in MIDI recorder, since notation software usually places restrictions on the MIDI implementation that can be used/supported for its files.
I would suggest either:
1. Use Finale with Hauptwerk as described in the 'Composing pieces off-line from MIDI notation software' section in the main Hauptwerk user guide (pages 229-233 in the current v5.0.1 version). For example, you could set up a 'spare' 'Hauptwerk (alt config N)' configuration (desktop short-cut) for use with Finale. Or:
2. Use a more flexible/general-purpose MIDI sequencer application instead of Finale, such as Cubase. You could then potentially use it to open MIDI files that Hauptwerk's built-in MIDI recorder had recorded, edit them (being careful to retain their MIDI implementations), export them as MIDI files, then open and play them in Hauptwerk's built-in MIDI player. The 'Recording | View Hauptwerk MIDI recorder/player fixed, predefined MIDI implementation (for this organ)' menu function within Hauptwerk shows the MIDI implementation the the MIDI files would be in (and would need to remain in). The significant disadvantage of this approach is that you wouldn't be able to play the MIDI files from the MIDI sequencer as you edited them, so you would effectively be editing them 'blind'.
I'd recommend option 1, especially if you already have Finale and prefer to use dedicated notation software over generic MIDI sequencers.