As already said, #2 works because you certainly can Compel with the situation or location aspect.
#4 also is very relevant. Compel doesn't necessarily have to be the only option. There are ways to manage your main complaint about anticipating a long string of Overcome attempts as a player tries to maneuver their character out of being forced to reveal the truth.
Simplify mechanics while supporting story texture.
I know that Fate appeals to people who want to roleplay (RP) things out. It's certainly possible to RP out all the lies someone wants to attempt, while not letting the Zone of Truth become a tar-pit of lie rolls. There are a couple of options.
Determine the stakes.
Remember to roll the dice only when both success and failure are each potentially interesting to the story. Make sure the players know why they're in it, and don't let it spin aimlessly as they try to turn it into a long string of lie attempts just because they feel like they have to win it. It's possible to locate part of a scene in the Zone of Truth without really demanding much conflict or making players feel like they're expected to grind their way through it. On the other hand, it's definitely a great dramatic element, so, when the direction of the story really does hang on a turning point in the Zone, that point of drama should be clear enough that it's identifiable as a single focus, which you can then spend as much or as little play time on as the story calls for.
Page 200 of Chapter 8, on Running the Game, describes reducing the stakes of the scene to a single roll, and this doesn't at all rule out the RP possibilities. It's a zoom-out from the point of view of the mechanics wrangling, but doesn't say you have to zoom out of the RP.
Create a Challenge.
Chapter 7, Challenges, Contests, and Conflicts is described entirely as a set of tools for zooming in on the stakes and highlighting the specific points of drama which lead to the outcome. If you, or your player(s), want the stakes of a particular visit to the Zone of Truth to really be determined by the maneuvering of the character's thoughts or statements, use the Challenge mechanic to give the player the opportunity to narrate their lies and exercise different parts of their character's sheet (skills, Aspects, stunts). Yes, this does mean there will be more than one roll, but it will be manageable, by-design, and not an unlimited scope for whatever the player can think to try before the stakes are won (or lost, as the case may be).
Take those Fate points.
In Fate, obstacles, problems, or achievements which are very important to the player come down to "How bad do you want it." Fate points are limited enough that it's a built-in limitation to how many times a player can really crank on a problem. GMs should not drag scenes out till they have wrung all of the Fate points out of the player(s) and then continued to call for rolls. So with the above ideas about structuring the scene around a specific stake in such a way that there's only a finite number of rolls before the outcome is revealed, be free to go ahead and make it hard. The Zone of Truth shouldn't be easy to beat. As GM, one of my phrases I use with players is, "How bad do you want it?" but I only use it when stakes are interesting either way (success or failure). Invoking Aspects or buying off Compels are narrative drama: Tell me how your character dodged that bullet and why it was a great bit of story to see that happen, and drop that Fate point in the cup as your thanks for my giving your character a chance to be awesome (Fate Core, page 4, page 88, page 210).