How Do I Power A 220 Water Heater Off Two 110 Breakers
You cannot get 220VAC from one leg in your panel. You must have two isolated 120VAC legs to do this. Using two single pole breakers on one leg will still only give you 120VAC.

Why can't you have the main breaker replaced? You should be able to buy a replacement breaker without replacing the whole panel.  Also, have you tried manually setting the magnets in the main breaker? This is done by removing it and slamming it hard down on all axis. This will sometimes physically reset the magnets in their proper position within the breaker and restore normal operation. They can sometimes be jarred out of position when tripped. But since you have to remove the breaker to do this trick, you might as well replace it with a fresh new one.