The solution may be to design your site and test in Internet Explorer before even looking at it in any other browser. It might be faster for you to resolve the quirks in FireFox & Chrome then IE. Reversing your process might speed up your development time by 20%.
No, that introduces the same type of bias, just from the opposite direction. The key is to keep a broad range of browsers quickly on hand to regularly check _while_ you develop.
There's no reason not to have multiple browsers quickly available - modern computers have sufficient processing power to run multiple applications simultaneously these days.
