I’d just replace the clock display with a text object: then it should be possible to use Blender Python API to update its value based on time or the current frame. This example of writing into a text object is pretty old (Blender 2.6) but who knows: it may still at least suggest the right direction; this one isn’t much newer (2.81) but shows a workaround for a possible issue with updating a text object on every frame; and that one (9 years old – which version was current then?) shows several short practical examples of showing the current frame, etc.
The challenge would be to find a suitable font – but since the clock isn’t very close, it doesn’t have to be perfect.