As PeterB suggested, Harliquin is a fine understudy for Cointreau. For me it's about tasting the heritage cocktail, as close as possible. You owe it to yourself to at least try it (without the hype -- canned sour mixes, added fruit flavors, cheaper ingredients...). The essence is the taste of Tequilla, supported mildly by lime and the liqueur.
I can immediately tell the difference between a regular triple sec and one of the finer orange liqueurs. I'm easily distracted by shiny objects and I still think those colorful curacaos are a waste of time.
The chow recipe seems solid. Try it with Harliquin (or comparable). I rim my glass with the spent lime and then sprinkle or dip in kosher salt. Sometimes I even dash some salt in before shaking. The salt (along with the lime) enhances the Tequilla flavor.
If it's not sweet enough, try half a teaspoon of powdered sugar (adjust to taste) to the mix.
Like any classic cocktail, quality ingredients and accurate measurements are key.