I would have said that having more different engines like Opera would make your job easier, not harder. After all the more different engines you test with, the greater the chance of finding problems - which may not show up immediately under popular browsers, but might cause the site to break a couple of years from now when newer browsers become popular, because you inadvertently relied on some non-standard behaviour or implementation quirk. (If your site breaks with browser X, some of the time it will be because of bugs in X, but at least half the time it will be because of bugs in the site's code, assuming X is not hopelessly ancient or non-standard.)
After all, the purpose of testing is to find bugs, and anything that helps you find more of them is a good thing. But you seem to be approaching it from the other way: you see the testing process as a way to prove that something works (rather than finding ways in which it doesn't work), and thus by testing less exhaustively you can find fewer problems and go home earlier.