Spoke tension - is a left tilt ok to prevent explosion?
Your wheel is overtensioned. That is not good as it will eventually lead to premature failure somewhere, maybe worse than you're currently experiencing.
In the case of wheels that don't come as manufacturers' sets, ie the spokes, hubs, and rims were all purchased separately, the spoke and the rim and even the hub are going to have different maximum tensions. In this case if you overtension the rim it will either not stay true or crack at the spoke holes- in extreme cases it can even encourage the wheel to taco under less lateral load. If the spokes are overtensioned they will eventually snap. Should the hub have the lowest maximum tension and you overtension it you run the risk of breaking the hub flange.
In the case where the wheel comes as a manufacturer's set (for example, many high end Mavic and Shimano wheelsets have compoenents that are all proprietary and only work with a given wheelset), you're going to have a maximum tension which is still going to be limited by one of the aforementioned components but you likely wont know which one. Same rules apply though- something will prematurely fail if you keep the wheel overtensioned.  
You need to let the tension down instead of bringing it up to get the dish correct. How old are your wheels? If they're relatively new you may have a warranty issue on your hand, although you may have voided said warranty by overtensioning the wheel. If the wheels are old, it's important that spokes have a fatigue life just like everything else and you may be hitting it. Often when you get close to the fatigue life of the spokes on your wheel you'll bust one after another until you relace the wheel.