The target has to know the spell is being cast and the magic itself doesn't let them know. Nobody in their right mind would voluntarily fail a save against unknown magic.
If you know your magic-using friend is trying to rescue you....not hard to put two and two together. Doubly so with, I dunno, the judicious application of
sending? E.g. "In exactly one hour from your reply, I will cast
scrying on you. Please voluntarily comply. We will teleport in and rescue you. Reply now." You'd need to be "familiar" with this person, but given the context of things like
teleport and
scrying, there are explicitly methods to become familiar without direct contact--and if you've been hired to rescue someone, it's a pretty safe bet you can ask the people who want to rescue them what you need to know to be familiar, and alter the 25-word message accordingly. (E.g. "<relative> wants to rescue you, saying <some identifying statement of no more than nine words.> In one hour, I'll cast scrying. Please comply. Reply now.")
First, the target has to fail the save against the unknown magic. Second, I don't see anything that says 10 minutes is enough time to study a place carefully. The other part of that description is a place that you've been to very often, which very strongly implies you have a hell of a lot more time spent there getting to know it than 10 minutes.
So, we're right back to "nerf it into the ground to prevent it from being useful" territory, yet again. The text simply says:
"Very familiar" is a place you have been very often, a place you have carefully studied, or a place you can see when you cast the spell. "Seen casually" is someplace you have seen more than once but with which you aren't very familiar. "Viewed once" is a place you have seen once, possibly using magic. "Description" is a place whose location and appearance you know through someone else's description, perhaps from a map.
Given that? Fine. Cast it while you still have
scrying active. By your own admission, you can see the location, and the text for
teleport (as quoted above) explicitly says "a place you can see when you cast the spell."
Teleport doesn't require concentration, so you can cast it while still having
scrying active.
And I don’t think it’s adversarial DMing to be a bit tough on the interpretation of spells. Some of you guys complain about how powerful casters and high level spells are. Well, the more power, the more oversight things require (now if only we had that with certain aspects of society around us that are a bit to amok).
The point is that you feel you have to. You feel you
must legislate well beyond the text of the rules, inserting a bunch of extra requirements, pushing things to the absolute limit of what you as DM can get away with in order to punish the player for using a powerful tool effectively.
Why not make the tools so you don't feel the need to do that?