An antimagic field would not prevent you from doing any of those things, unless it extended deeper into the earth than you could tunnel, higher into the sky than you could fly, or farther than you could teleport.
To accurately match the situation as we perceived it (with our resources at hand), the size of this antimagic field was big - or the goal we wanted to achieve was very close to the lava river. Whatever.
Check out the Black Company books by Glen Cook. They're excellent, and random death abounds.
The Torg books also fit. But then, they are based on the Torg game rules, and it's no surprise that a game-inspired books has "gamey" scenes, so your Black Company books might fit better. But it is still the exception, not a rule.
An issue not related to the "sitting out" thing I see with Save or Die (especially in the case of the Medusa): There are no saving throws in the story world. Either you are prepared with a special mirror and know how to make the Medusa fall asleep, or you are not and just turn to stone upon seeing her face. There is no "saving throw" against the effect.
Entire hordes of non-protagonists will just turn to stone if they meet a Medusa. Only the protagonist will find a way to avoid - not save - her power.
The closest to a saving throw we might get to see in fantasy is resisting mind control - and usually that only happens if someone is talking the victim down and reminding it of its real loyalities or personality.
In a way, the save or die approach is also making you into someone that _might_ be a fantasy hero - but maybe you're not, and you're actually just a side-kick that dies to make a story point - this is a dire situation for our real hero (the one that made his save.)
Well, since I am living out my power fantasies when playing D&D, I am already assuming I am a protagonist, not the side-kick. Save or Die tells me this assumption is wrong.