In my experience, the number one obstacle to strategic thinking is that people tend to confuse their impulses to virtue signaling with their actual goals. People tend to be very strategic about actual terminal goals: that is, things they genuinely desire, in the same way as one might desire ice cream when hungry, or air while drowning.
So my go-to tactic for helping someone to be more strategic is to test their desire: can they actually experience the in-the-torso feelings that are strongly correlated with desire and pleasure, when thinking about the goal?
If not, they probably do not have a terminal outcome that is actually desired, and instead are being confused by their brain's attempt to signal virtue, solve a perceived problem, or reduce cognitive dissonance.
(By "signal virtue", btw, I don't just mean conspicuous displays of morality, but also things like following in parents' footsteps or trying to live up to the expectations of others, trying to justify one's existence or purpose, and rather a wide variety of other weird things brains do to promote or maintain perceived self-worth and/or social standing.)
Anyway, when humans appear (in my biased sample of experiences) to not be being consciously strategic, it is generally because they are being unconsciously strategic about achieving an entirely different goal than the one they believe they're trying to achieve. And the goal they consciously believe they're seeking is in fact the result of their brain's strategic planning, rather than the input to another round of such planning.
The ultimate goal of such things is usually "to be a good, worthy, lovable person who visibly cares about the right things according to the value system(s) I have internalized".
Such goals, however, seem to run on different hardware than practical, desire-based goals. And if the non-desire-based goal is based on an idea that one "should" be a particular way, then it becomes virtually impossible to trigger the desire-based machinery at all.
(Because it is very hard to feel desire for something you believe you're already supposed to have done, had, or been.)
So.... if you want to be practically strategic, the very first step is to make sure you know what you want and why you want it. If the real goal cannot be defined in terms of a concrete observable outcome in external reality, that you can actually physically feel some form of pleasure at the idea of attaining (vs. merely feeling an anxious need to have), there is little point in going forward with any strategic planning, because strategic planning and social signalling tend to be mutually incompatible.
(Because our "desire to signal" wants to make our signalling-driven desires appear "honest", i.e. that they're not being done in order to signal.)
This makes it difficult to notice at first glance when we're doing so, so the desire test (aka the "mmmm" test", as in, "can you think about this in a way that makes you sound like you're enjoying yourself?") is a hack to work around this potential for self-deception. Our signaling desires seem to be injected on a different subsystem of the brain (maybe by rewarding certain directions of thought directly?) than the one that is used to pursue tangible desires like food or mates.
Food and mates make our mouths water or bellies rumble. Rest and safety make us go "ahhh" and relax. All of these pleasurable feelings arise from tangible goals, and motivate us to actually pursue them.
This one insight is, in my experience, worth a thousand abstract treatises on planning or decision-making. If you try to apply such ideas while actually pursuing a goal to virtue-signal, resolve cognitive dissonance, or fight something that seems "wrong", you're virtually guaranteed to use them in ways that will subtly sabotage any real action. (See, for example, all the vaccine distribution issues stemming from virtue signaling -- we are not immune to doing this sort of thing just because we label ourselves rationalists.)
Where are all the comedians in the club when they're not on stage? They're not in the green room, they're all standing up the back watching everyone else perform.
A single strategy alone is a typically a sub optimal strategy. IRL you don't typically act out LW thought experiments with the expectation they'll work out.
There's no substitute for practicing at whatever activity it is you're trying to master, but it isn't the only thing to it. People study all the time. We call that education and find it so useful that we've made it compulsory for minors.
I would argue that "do the same thing that many others did to achieve their success" is a blatantly obvious strategy.
The only way to guarantee that you don't get an answer to a question is to never ask the question.
Saying no may be your weak point, that is not the case for others. The most obvious strategy in that general situation is "no, but what can you offer me to change that to a yes?". That alters the dynamic of the negotiation in a way that can be useful. Besides, IME a hard no is never a negotiation.