I feel like "figure out the constraints of your problem" is an incredibly general problem solving tip. "Not knowing the constraints" is very close to "being unable to easily distinguish a solution from a failed attempt", and you can't solve anything if you don't know what a solution looks like. 

Identifying the goals, constraints, and variables subject to minmaxing is the first step in any problem solving, and if you can skip that, it's usually because you already have an intuitive idea that's close enough to correct that the best solution within your intuitive model of the constraints is also a solution in the true constraints

I think in your UI example, one way to look at what happened is to say "you had a mental model of the constraints of the problem which excluded certain possibilities which were actually ideal, and included certain possibilities which were subpar, leading you to not find the part of the solution space that was optimal, because your mental model of the problem didn't have it as an option".

On the other side, knowing what an ideal solution looks like often makes the solution simply fall out as a matter of course. If I'm fine-tuning the level up XP thresholds in an RPG style game, and I know the ideal solution will make it so that as I level up and monters drop more XP, I spend the same amount of real time on each level, then the very act of thinking about it in terms of the solution makes the formula obvious: just take the amount of XP monsters at this level give you, multiply it by the number you can kill in a given time frame, and there's your number. Admittedly this is a pretty simple example with only one working solution, but oftentimes when I face a difficult puzzle and learn the solution, it turns out the solution violated some constraint I had accidentally assumed, like a key I assumed had to go into a lock is instead used as a wall, or a gap I assume required a bridge to cross instead only needed a well timed jump. 

So I guess in thesis: understand constraints, figure out what the solution will look like before you waste time trying things (not before you try things, just before you waste time trying them), and if you feel like you don't understand the problem, fix that before you continue

I couldn't follow a lot of this, but it led me to examine my own beliefs about honesty and when I should be honest, and made me realize that unless you fear imminent harm like the gestapo example, you should never lie about what you are and are not willing to lie or glommerize about, but you should glommerize quite a bit on the subject of what you'd lie about.