Perhaps part of the problem is that you see fallacies as a tool for debate (given your comment about getting the upper hand). Logic -- from informal to formal -- is not just about defending your own beliefs, and shooting down other's arguments. It is also about assessing your own beliefs. There are various terms for this by different philosophers, probably the best term I've heard is contrasting weak-sense and strong-sense critical thinking (this is from Asking the Right Questions by Keeley and Brown). Weak-sense is using critical thinking as a tool of attack. Strong-sense is using it on all beliefs, especially your own.
Given this view, it should perhaps become a bit more clear that there are logical strategies focusing on "anti-fallacious" techniques. Those strategies are the former methods you used as a blunt tool to beat people over the head with (now used as a tool of self-reflection, and attacking your own ideas).
More specifically, there are various tools out there for constructive argument. Probably the most common from informal logic is argument mapping, argument diagramming, and deep analysis (all similar terms). Usually, these tools are used to analyse other's arguments, but they can be used as a proactive tool (I've heard of one PhD philosophy student that did an argument map of his entire thesis, which is pretty damn hardcore). If you are looking for textbooks, Douglas Walton's Argument Structure covers this indepth. If you want another book Understanding Arguments by Fogelin also covers argument mapping of informal arguments. On the formal side of logic, there are valid argument forms, like modus ponens ("validity" here being strictly defined). Picking up any formal logic book will go into these forms in detail. Howson's Logic with Trees is good. Sainsbury's Logical Forms is another, which goes indepth into the notion of what is good form in formal logic. Some Discrete Mathematics books are excellent as well, like Epp's Discrete Mathematics with applications, which has a chapter on valid argument forms (chapter 1.3 from memory).
As to general sorts of strategies I can give you some tips, but these tips are part of a larger context of philosophical writing and critical thinking in general, so the following strategy doesn't take into consideration things like finding the issue, or analysis of an issue/question, or how it might interact with other philosophical areas (epistemology, ethics, metaphysics, philosophy of language). Here is my general strategy for logical thinking:
(1) Start with reasons, then draw your conclusions based on what your reasons are. Starting with conclusions and looking for reasons to support them is pretty bad form, and is at the root of many poor arguments. Having trouble coming up with ideas? Check out (6) below. It's important at this stage not to get caught up in analysis of your reasons ("paralysis by analysis"). Leave that for (3) and (4).
(2) Once you have a bunch of reasons, and start to form some conclusions based on these reasons, you can start grouping together reasons and conclusions into sub-arguments.
(3) Start thinking about refutations of (2). Are any of the reasons false? Do the conclusions lead to absurd results? Is the argument valid? "Valid" here being strictly defined, in other words does the conclusion follow from the reasons? If your argument is more inductive-based ask yourself if there are "fresh" reasons (inductive arguments can be weakened at any time by a body of background knowledge unrelated to the structure of the argument. E.g. you might have a great argument based on some science, but you have to keep in the back of your mind that there is a large body of knowledge out there, and any one observation could weaken your conclusion). Another important question concerns metaphysics and epistemology. Is there something in your argument that you are committed to that is inconsistent with another belief you hold? Perhaps something that isn't even part of the arguments you are considering? As an example, take the topic of free will. You could make several arguments about free will, but have you considered the larger web of beliefs that you hold? Perhaps your argument on free will is inconsistent with your beliefs on political philosophy. There are multiple other questions here that could take up thousands of words. Pick up one of the above books for more.
(4) Can you find ways to defend the points raised in (3) against your original arguments in (2)? Do you need to weaken your conclusions? Can you outright discount these refutations? Do you need to get rid of certain reasons, or entire sub-arguments?
(5) Arrange the sub-arguments, refutations, and protection against refutations into a larger form. At this stage a larger conclusion or thesis should be in your mind. Don't forget to add "indicator words" to your arguments, so your argument is as clear as possible. Lists of indicator words can be found in the informal logic texts above. As a shortlist you have reason markers ('as', 'because'), conclusion markers ('therefore', 'thus', 'so'), and refutation markers ('nevertheless', 'nonetheless').
(6) At this stage you can start thinking about style. Rhetoric gets a bad rap here, but classical rhetoric is excellent for larger structure of arguments, and may also help with "argument discovery" in (1) and (2). Check out this page for more help on argument discovery (known as Topoi in rhetoric). Don't forget that there is more to argument discovery than the topoi. Research also comes into play. For larger structure of your document, this page will also help (known as dispositio in rhetoric).
Finally, the best way to get better at spotting your own fallacies, is to be on the lookout for other people's faulty arguments. You want a three pronged strategy for this. You don't just want to go around finding faulty arguments from bad arguers; though this helps at the beginning as you cut your teeth on logical tools. You also want to read the best arguments on the planet by philosophers, scientist, jurists, and others. You also want to find average arguments from everyday people. So the strategy for practice is this:
(i) Find bad arguments. In one of my critical reasoning classes we did analysis of conspiracy theories. Wikipedia's list of conspiracy theories would be a good jump off point into practice of argument mapping and analysis.
(ii) Find average arguments. Look into your local paper in the editorial and letters section. These arguments will range from good to bad.
(iii) Find good arguments (though there is no guarantee that they are good, as you will soon learn), look into books published by university presses, or look into long form journalism, or essayists. Look into writing by philosophers. Look at popular science books.
There are also two good books I can recommend on this. Readings for Logical Analysis by Kelley and Hicks, and Analyzing informal fallacies by Engel. Both have a ton of arguments available for practice.