These questions are academic in the end, and never mind the academic credentials of the heroes.
What happened? First there was the (as such harebrained) Plan A where Sphere Data was supposed to be amenable to being moved from place to place even though it refused to be erased. It took time and effort to attempt this plan, which Control subverted to its needs and got a good chunk of the data (but did the corresponding chunk really disappear from the ship's files?). Then the heroes understood that Control would be breathing on their necks if they tried that again, so they went for the (very sensible) Plan B of simply blowing up the ship, no effort or hurry or risk involved.
But then the data refuses to be blown up, and our heroes realize it is resourceful and essentially immortal and best not antagonized further - one hostile AI is already plenty. So their next plan is A again, and no doubt they will buy time with diversionary jumps if there's a need.
But what happens at that point? Our heroes decide that Season 2 has unfolded for a reason. They decide that the fact they possess a time crystal dictates that they time travel. And when they sensibly debate whether this is a prudent way to deal with the curveballs the universe throws at them, or mere insanity, they get a Red Sign.
It would be pretty silly not to believe in divine guidance at that point. So they go to the Sign, and get obvious help to go with the divine plan. And while there, they get a second ETA for the arrival of Control's dispersed assets, so they can actually be pretty confident in their ETAs. And then they have to decide whether the hiatus on jumping dictated by the divine plan is a dangerous liability when the ETA already allows them to proceed without further jumping.
So this, the orbit of Xahea, is the first true time of choosing.
I) A giant leap to the other side of the universe so that the plan can be executed away from Control's prying nanites? (But that would be a jump to the unknown, possibly to even greater danger. And that would be danger to the crew and perhaps mankind, but not to the Sphere Data which, lamentably, is immortal.)
II) Another short and controlled leap, again resetting the ETA for an extra day or so? (The dangers would be better known, but this would still mean leaving the Enterprise behind.)
III) A leap to Earth, where Starfleet could provide protection while the plan was executed, or perhaps modified with help from UFP's foremost experts? (But that would expose Earth to this deadly game, and the heroes to S31's supposed strong presence at Earth, and thus perhaps serve the enemy, just like the original attempt at Plan A did. The whole point of asking the Enterprise alone to pick up the Discovery crew before scuttling was that Pike couldn't trust anybody else.)
To go for II, the middle road, might be playing it safe. But it's not the on-the-spot decision our heroes would be making, not when they have so much reason to put their faith in divine guidance. At best, it's hindsight and armchair quarterbacking, which of course is what the audience always does by the very definition... So, "none of the above" is a fine decision, and it's too bad Queen Po couldn't keep her promise on finishing before the known ETA.
Timo Saloniemi