Shopping isn't going to take that long. They should do tourist things!
There are shuttle tours available - circle the planet a few times, land at neat spots on the way, have the run thereof till takeoff. They can just sign up for one that takes a week and be back at the port before Harlequin is. But not by much! Hello again, Harlequin.
He finds a buyer - a museum on Earth who is willing to cover shipping in order to get their hands on one of humanity's first homegrown warp-capable ships. (The Harlequin continues to stubbornly refuse to fire up its own warp drive, so it'll need to be transported as cargo.)
He methodically goes through the ship taking out all the things that are his and packing them onto the Prometheus, since he has the chance. This mostly amounts to more clothes, and some other odds and ends. Then he says goodbye and sends it on.
Also, as he is cleaning it out, the Harlequin suffers another system failure and all its computer systems are completely scrambled; he has to format them back to factory settings. Oh, well, the museum wasn't buying it for the data.
Eventually the computer spits back confident reports on how to translate warp equations into local tongues, and on who fails to be above plagiarism, but Isabella has yet to decide whether to seed the plans among several of the planet's nations or just one. She doesn't want them to start fighting over it on the eve of post-scarcity.
"I'm tempted to distribute plans to three scientists from this northern country here," she says, pointing at a map of the planet. "It has the most currently Federation-friendly culture, and it could self-support building the drive. But there are candidates from here, and here," she points at two more. "And if I give it out to more than one political unit, they're having a race, whether they know it right away or not, and races can get heated."
"You could end up with a race even if you didn't mean to," he points out. "Once somebody knows it can be done, if they're smart enough to figure out how, they will. Whoever you drop it on, they're probably going to publish about it, and not everybody who reads them is going to be from the same culture."
The species on this planet is nocturnal, so she sets a timer for the earlier sunrise of the two time zones to remind her to start scanning for life signs in the narrow area in question so she can beam down unsupervised.
That leaves a couple hours to draw up the plans in that language, if she wants to get it done today. Out comes the paper and the pens. Blank paper costs, but not all that much - it's compact and easy to make and nonperishable.
Isabella has a procedure here. She doesn't want to be caught on security cameras. She could just beam the plans down, but it would be hard to get them precisely targeted. She has a nice concealing outfit and a mini-EMP to disable surveillance devices long enough to find someone's desk and plunk down her gifts.
They are presently out of the system and warping along to the next. Isabella falsifies her records. "...Say, do you want to double-check my track-covering? No one's actually dug suspiciously around in my travel logs so I don't know if I'm doing a competent job at making it look like I wasn't around when 'warp was discovered' in the relevant systems."
Isabella's logs show - at least to casual inspection - that while she has visited all the systems that have mysteriously acquired warp (except for El'el Prime, which acquired warp while she was active but is not listed at all), it was never at the right time (except once when it was; it would not do to always be slightly off). Sometimes she finishes her surveys of those systems a week before, sometimes a month later.
"You should probably arrange to not have visited more of them," he comments. "Even with shifting the timing, it's a pattern, and it's not like there's a crowd of other ships visiting these systems that you can get lost in. There's the problem of refueling history, but I'm sure we can figure out a way around that if we try."
"You know," he says, "I could probably lead a less risky life if I tried really hard, but I don't actually set out to be captured by Klingons or robbed at gunpoint or almost raped or whatever. These things happen by accident. They're not so common in the world we live in now - well, Klingons are a special case - but I was born in a very different world. How much do you even know about prewarp Earth?"
"Imagine you're completely alone," he says softly. "If anyone you meet finds out anything true about who you are or where you came from, and gets to the authorities with it, you'll probably be killed. But you have to get money from somewhere, because nothing's free, and you're not sure if you can starve to death but you don't want to find out by trying it. You speak a dozen languages and you're familiar with thousands of years of cultural and political and military history from all over the planet, but nobody ever taught you how to get a job, cook, wash the dishes, do laundry, buy something from a store... you have to figure all that out by yourself, and hope nobody gets suspicious if you do it wrong. That's the world I grew up in. With crime rates hundreds of times what you're used to. 'I avoid situations where I might have to kill somebody' is the kind of thing you only say when you've never had to choose between the street where you'll probably get mugged and the street where you'll probably get arrested."