I am replying to myself. Only now spoted this point in the Forum FAQ:
which says: "Set an 'Expect completed by' date in the Activity completion section of your forum."
I have just tested this for an LTI tool, and it also works - for the end date at least.
(In fact this (workaround) method works with most other modules that have problems communicating their deadlines and opening dates to the Course overview, or those that don't have Availability / Timing setings.)
Good to have a solution for external tools on the Moodle side !