From the point of view of an SE player I would choose option D (hehe)
Option D) As two characters cannot share the same square, and jumping a pit has a chance of failure that would result in two characters sharing the same then you cannot attempt to jump an occupied pit and would have to wait until the other character moves out of it (or if they are an opponent then attack them when they are down!)
Much longer answer … I suppose that this really boils down to “How deep is a pit?”
In real life a trap that involves the combination of a hole in the ground and one or more sharpened spikes or stakes can vary in depth from 1m to several metres deep and the depth of the HQ pit traps isn't stated in the rulebook.
There are loads of different variants (“trou de loup / wolf hole", a tiger pit, punji trap, stake trap, roman "lilies") all the way up to a traditional large trapping pit but essentially, they fall into two categories
1) Those intended to temporarily disable an attacker (trap them) to slow down an attack (the HQ Pit rules achieves that) and ideally either force their colleagues to help get them out and call in a rescue/extraction (not relevant to HQ) or to make them vulnerable to defenders (very relevant to HQ - the 1 less attack dice whilst in a pit does make the victim more vulnerable to a defender)
2) Those designed to kill or failing that trap the victim until such time as the trappers returned. Importantly for these to be effective they would have to be well over 2m deep AND crucially too wide in either dimension for a victim to be able to brace themselves so that they could climb out, i.e., they were designed very hard to escape from
Our pit traps in HQ clearly are not of type 2, amply demonstrated by the fact that the rules state that not only can a Hero get out unaided but doing so is sufficiently easy that it doesn't cost them a single lost movement point or a lost movement die, and that they only cover a single square ~5 feet across in either direction maximum.
Based on this logic I have done the following in my house rules for standard (shallow) pit traps.
As a hero, once in a pit, you may search the pit for treasure or secret doors as if it were a separate room unto itself.
Scrap the above rule (granted treasure could conceivable be in a pit trap, from a previous, now dead, occupant, but that would be the same as any other square and could be called out in the Quest notes if needed – the idea of finding a hazard inside a pit trap especially a second pit trap seems daft, same for secret doors – really how secret do you want a secret door to be!)
Exceptions: When on the stairs or in pit traps, sharing a square is permitted.
Scrap the exception above (for both stairs tile and pit traps whilst we are at it)
Effectively limiting pit trap “occupants” to one, once someone is trapped in it then the square is blocked no one else can enter/pass through that square – you obviously can’t step aside to let someone pass if you are trapped
These changes, scrapping a one-line exception to a rule that isn't needed and scrapping a single stand alone line of text, seem to me to be the simplest way of resolving this issue and for HQ simple is best.
Finally, it sets up the option to have a proper large version of the pit trap as a special feature in a quest, at least 2x2 squares or even an entire room that plunges you several meters down, does some real damage, into an actual genuine separate room with all the normal room rules around treasure, traps, and secret doors that you cannot get out of (without finding the secret door), you could even through in some Undead previous victims for added spice