A few thoughts and observations:
- Thinking in strict sense is slow by nature. The only way to make it faster is to avoid it, that is to simply know the stuff. The more you know, the faster you think, that is do what looks like thinking.
- Emotions may disrupt any expert; you'll forget what is 3 by 5. There's a comment here already that mentions it, and I second it, because I was that guy. One of best decisions in my life was going to a shrink :)
- There's a structured approach to problem solving; formulate the problem (current state), the goal (the desired state), list alternatives, weigh them, choose. This may sound obvious, but a lot of otherwise smart people do not do this and simply pick the first idea that pops to their minds. Changing to structured problem solving helps immensely; it's actually used as a therapy.
- Some high-level heuristics may help: six thinking hats, TRIZ (although this one doesn't think it's a heuristic), morphological analysis, and so on. Their primary purpose is exactly that: quickly generate many different ideas and views and make sure to cover as many important bases as possible. Each has a special flavor; TRIZ, for example, aims for elegant minimalist solutions.
- Every blessing has a curse. I once read "Vengeance: The True Story of an Israeli Counter-Terrorist Team" (it was made into the "Munich" movie) and there was an episode when a Soviet special agent got killed primarily because he was a trained special agent who is always ready and aware of what's going on. Quick thinking looks very useful, but there will be situations when it isn't.