I have an idea.
In Drives R Us, I used a Condition structure on Hope:
STAR 0
FLAG existing
PLNT hope
ITEM wp_2bbeamlasr
END STAR
CONDITION 0
TYPE homeworld
STR0 terran
END CONDITION
PAGE 0
REQ0 0
ACTN endquest
ITMS 2 tech
END PAGE
If I'm remembering my thought process from two years ago, I originally tried a simpler structure, more like what you wrote.
I found that without the CONDITION block and the REQ0 line, it wasn't triggering. Also, without some item being always placed at Hope, the random items wouldn't appear. It really puzzled me as to why the homeworld trigger would have to work that way, but IIRC, it did.
You might try putting in something similar, and seeing if it works then.
Another option is to fall back on having it trigger when some other random star is explored, but add an ITEM command to the STAR block so there's an object on the planet when you get there. If you gave each of the five quests a different totally normal object from the main game, the player wouldn't immediately know that anything else had been triggered.
If I think of anything else relevant, I'll let you know.