Not a wholly ridiculous idea but what about a sequence where you win the piece back in 2, 3 or 4 moves etc. And also you cannot sacrifice to force mate.
Sudden death.

Not a wholly ridiculous idea but what about a sequence where you win the piece back in 2, 3 or 4 moves etc. And also you cannot sacrifice to force mate.
The game will continue if exchanges results in equal material, but once a capture takes place the oponent must recapture. If the recapture results in an imbalance in favour of the first player then the game is over. It the imbalance is the other way around then the first player must recapture in the next move or loose the game.
Off cource there will be situations where the recapture only can take place after an in beween move but for simplicity, i think the above rules will suffice.
After all the whole idea is to be better at not hanging you stuff and should be regarded as a training tool (for week players).
The point of sacrifice to force mate is a good one. Im sure that could be incorporated in the rules (if your opponent captures you have to win back material or win by check mate in the next move).

Off course there are other issues aswell, like gambits that would result in a loss. Maybe the easiest thing is to do this training on your own against the computer. Here is an example of a game I did against stock fish at level 10. As you can see I was overpowered at the end and decided to finish the thing before the decisive material loss. But holding on against a "super grandmaster" for this many moves just by not hanging pieces is a revelation. I guess the moral could be: Forget all about opening, positional play an all other fancy stuff until you stop hanging stuff.
You don't need another chess variant in order to train for not hanging stuff.
Few tips:
1. Solve tactics puzzles slowly. If you are in Tactics Trainer here ignore the clock completely. Otherwise use Chesstempo, books, databases.
2. Play slow games.
3. Work on you thought process. Always try to consider possible opponent replies.
4. Play against the computer like in your post #4 and try to hold as long as you can.
You say "Forget all about opening, positional play". I disagree. Positional errors like 12.Nh3 in your game from post #4 lead to material losses at the end.

You say "Forget all about opening, positional play". I disagree. Positional errors like 12.Nh3 in your game from post #4 lead to material losses at the end.
I agree. Positional errors will result in material loss and eventually the game. So when able to play without imediate, catastrophic blunders, then its time to try to master more advanced things.
Thanks for your insights.
One of the biggest issues weeker players (like myself) is facing is the tendency to hang stuff all over the place.
I would really like to see a variant of chess that could be called "sudden death" that follows normal rules exept the game is over as soon as one player looses material without beeing able to equalize right away. The first capture must be answered with a direct recapture.
First off all it would be great practice and probably lead to stronger play.