When I try to configure Win+Shift+Left for "Move Window to Previous Monitor" and vice-versa, I get:

The Key Combination bind failed.
The Key Combination is already in use. There are a few reasons why this can happen:
- The Key Combination is already assigned elsewhere in this application
- Another application is already using this Key Combination
- A built-in Windows function is using this Key Combination

However, I noticed that Fancy Zones PowerToy does support overriding the default Windows behavior to move across zones via its "Override Windows Snap hotkeys (win+arrow) to move between zones" configuration option. That's also open source, so perhaps you could implement the same thing in DisplayFusion so that the standard Windows snap left/right keystroke could be used with DisplayFusion monitor splits?