Wow, thankfully I haven't experienced this while running LotFP. My group has come to enjoy the abuse and fuckery, and I think each sees it as a personal challenge to try and get a "one up" on the game world to come out ahead for once.
That said, I have loosened up some of my "That's the way it is!" attitude in the interest of people having a good time. In your above examples, I would have let the PC who was captured roll up a new character, at the very least controlling a 0-level henchman who has taken an interest in the scheme or some such matter, and then they could help plan their own rescue. (In the Referee book, Raggi says to get the player back in the game asap, and even though he's referring to death, I would assume this for anytime a player is unable to participate in the game.
I'm assuming that for the infinite staircase, all the PCs looked at the eye and there was nobody left to complete the ritual? At this point, I'd just say, "Your characters walk until they die of thirst. Roll up new ones." If there are still PCs left who can do the ritual, just keep repeating the important parts in the room. Sometimes they need to be hit over the head with things.
One last thing, I do let my players read the modules after a TPK, if there is no chance they'll interact with it again. For example, they explored a lot in Better Than Any Man, and when they all died, we decided to restart in England. Reading BTAM gave my players a much clearer idea of what LotFP was all about and got them more invested in the setting/system/world.