Logic isn't as useful as you make it out to be. There are far too many situations in real life in which the logical approach is nonsensical. There are far too many people who simply do not operate logically, and your attempts to apply logic will simply backfire.A rationalist's best bet is to establish a maxim that is legitimized by reason alone. On that note, Kant's categorical imperative is one such maxim: Can you will the action/decison in question a universal law? If not, it does not have reasonable justification. If I were a moralist, I would be a Kantian. However, I decided long ago that the business of ethics can be no business of mine since my comparative advantage is in logic and cost-benefit analysis.
The purpose of a universal principle such as the Golden Rule is that it allows society to exist in the first place, without having to explain to each and every person why it is beneficial ethical/moral policy. It's a fundamental teaching tool, such as when telling a child, "Would you like someone to do that to you? ... [child meekly answers no] ... Well, then you shouldn't do it to others." It's easily learned, and produces benefits simply by showing people how to avoid most potential (and inefficient) conflicts.
Something funny happens, when a Rational takes hold of a spiritual truth, encapsulated and phrased in a fairly simple way, and then interprets that simple statement entirely literally, as a logical, objective rule, rather than as a spiritual/ethical truth. Of course, the Golden Rule, interpreted in such an asinine manner, is nonsensical. Fortunately, most people aren't rational in that regard, however, and understand what it means without having to find every logical contradiction and paradox.