That doesn’t necessarily prove anything – she probably still had all her memories and knowledge in her head, just jumbled up and inaccessible until they clicked back into place as she was re-taught. Teaching someone from scratch would take longer, perhaps every bit as long as it takes today.
Heck, I’d want to zip through the transporter and emerge as a 12 year-old version of myself with all my adult memories intact. May as well get a fresh start, at least physically.
That’s one of those Reed Richards Is Useless things – even though in one ep they accidentally figured out that was possible, it never happened again. You would expect it would occur to somebody that this is the secret to immortality, and everybody in the Federation would start doing it ever 30 years or so.
Well, I’d like to rise on my own skills/intelligence/merits, but if that’s not possible, I’ll just be cheap and easy. 
The Borg have personal shields. Do shields not work on projectiles? I remember one episode where the Enterprise was attacked by lasers and Riker commented that those wouldn’t even penetrate the navigation shields. Now, I am assuming that the navigation shields are there to deflect debris, which is hard matter, so why wouldn’t a bullet bounce off a shield - once they adapted, of course.
It would probably be covered by the same laws against genetic engineering or using certain types of really, really horrible weapons.
Seek out 7of9 and teach her that concept we humans call Love.
Also, reprogram Data so he can use abbreviations…
if (speech==“Do not”){
speech=“Don’t”
}
My rules number 1 - never go in a transporter. It’s not a transporter, it’s a replicator which kills you and makes a copy.
Wow, talk about a Trekker’s dream!
Since the Federation seems to take care of everyone’s basic needs, I’d find an apartment with a replicator and an LCARS terminal, and read up on history since 2010, then see if anyone in my family line has survived, look them up and introduce myself. I’d like to take a tourist trip around the Solar System, esp. visiting the site of the Apollo 11 Moon landing.
Try out a holosuite, sure, and watch the archived post-2010 movies of my favorite stars.
I’d give my oral history to any historians who might be interested, and would see about maybe teaching a history course myself (“American political history, 1980-2010,” “The U.S. Presidency through 2010,” “Everyday life in the early 21st Century,” “The Straight Dope and Internet subcultures,” etc.).
Then I’d look into joining Starfleet - maybe the JAG Corps? Criminal law in Picard’s and Janeway’s day doesn’t seem all that different from our own, after all.
Maybe someone already suggested this, but I missed it if so.
I’d look up Q, and at least travel around with him like Vash did. He was one funny bastard, and I think we could have a good time exploring the galaxy and fucking with other species.
I would eventually hope to join the Continuum. Holosuites, holodecks, what? How bout I just become a god and remake reality as I see fit. Plus I’ve never been so keen on the whole dying thing, and as far as I know, Q don’t die.
Enlisting in Starfleet seems to be a dangerous decision. I think being part of a Vulcan science expedition or something else would be better. Maybe working with the Ferengi and trading - I don’t think they get picked on as much as the Federation.
And lastly, I’d look up some Orion slave girls, call up the Traveler, and have one hell of a party.
You may be either an obsessive crackpot who’s escaped from his keeper or a distant relative of Samuel T. Cogley, attorney-at-law!
These are the voyages of the Q. Our eternal mission: To explore strange new worlds. To seek out new life and new civilizations. To boldly annoy where no Q has annoyed before.
Well, when Q was stripped of his powers in “Déjà Q”, he was quite mortal and was in danger from the Calamarain. Then, there were the parents of Amanda Rogers, who were killed by a tornado (conjured up by the continuum) in Topeka, Kansas while in human form. Then there was Quinn from the Voyager episode “Death Wish” who became human and Q helped him to commit suicide. It seems you’re immortal as long as you remain omnipotent. Just don’t allow yourself to become human.
I bet the (TOS) Intrepid probably has a few openings for its next expedition.
Education.
Depending on where in the timeline I dropped in, I’d make it a point to look up at least one of the hot babes like Troi or Crusher and find out if she might be interested in experiencing hot 21st century monkey love.
And I would never, never, never put on a red shirt! 
Why can’t I be both? Don’t you oppress me!
It seems to be a muddle:
Work makes a short lived shield out of a communicator badge, and stopped Evil-Data’s bullets on the holodeck, in an old west street duel.
But then in First Contact, Borg shields don’t stop holographic bullets.
shrug
I must be weird. I’m genuinely surprised that I seem to be the only one who’d be trying to find a way home.
The OP said, “They cannot return you to your proper place in the multiverse.” Don’t fight the hypothetical!
Hey, I WROTE the OP. What I meant is that whatever civilian or Starfleet scientists you meant upon entering don’t know how to get you back to your proper reality, not that it’s categorically impossible. Of course I was trying to start the exact silly discussion that began; I’m just surprised that no one at all wants to go home.
Worf knew exactly what he would be facing and jerry-rigged his shield accordingly.
Picard’s gambit only worked because the Borg didn’t expect it, and he knew to show no mercy; any Borg that survived his initial volley was going to adapt & overcome.