Poker You both are bluffing, but he's got the better hand

Ever so often I encounter in turnaments or sit-and-go games players who I "know" are bluffing when I play against them. The obvious reaction is to extort as many chips as possible from them and finally go all-in in case they won't fold before the river.

A subset of this situation is when I am bluffing as well, but do so "better" or let's say more convincing than my opponent, for instance because I sit before him and can actively make the bets.

Most of the time these situations end well, because my opponent will fold when the price is too high. But then there are those few cases that have ruined entire tournaments for me which were going quite well until that point:

I am talking about players who are bluffing like Pinoccio, but who are also determined to pull it off to the end, despite having a big brown sausage on their hand. The problem is especially relevant with weak/new players who thing their ace+queen suited is still good when there are only numbers and jacks on the table.

How do you deal with that. do you go for the risk that your own big brown sausage is less smelly than the one of your opponent?

So far I really haven't found a solution to that problem, because:

1. Going all-in with 2-5 while having to rely 100% on the cards on the table is never a good option when you know your opponent will call.
2. Most hands with big bluffs against weak players drag to the river, meaning there's little room for a premature fold.
3. Checking and showing cards or even folding on the river is a very, very weak sign for all players on the table and gives the opponent even more reason to go berserk (=turn the entire game even more into a gambling session).

Who do you prevent that from happening, what's your tactic against that and how often does it happen to you?

...or maybe...

Is it perhaps I who is the fool in this situation, because an unhinged bluff against a better bluff is something one should avoid?

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