I personally really enjoy loose skillsystems and I think they offer excellent opportunities for players to be creative with problem solving. Two games that do loose and open ended skills really well (that I have played) would be Numenera and 13th age.

13th age goes all out with the open ended side. Players choose backgrounds and allocate points to them and if they can motivate why that background would be helpful in the current task they get the bonus. It has some pretty wacky effects which are great in the general wacky framework it's designed for. The tone you're going for in your game may make the 13th age apprioach rather inappropriate, but it goes a long way to showing that vague skills do have their place.

I really think you might benefit from taking a closer look at the skills system in Numenera though, since there seems to be a fairly natural analogy to a lot of what you're mentioning here. In Numenera you generally get skills from a class or trait, which makes them a lot more controlled than their counterparts in 13th age. What Numenera does that is very nifty is that it allows skills to have overlapping domains. E.g. I once played with a character skilled in repairing and in electronic devices, both of which very naturally lend themselves to being useful when repairing an electric device - and in numenera the bonuses from the skills would stack. There isn't really a hard drawn limit in Numenera as to how broad or narrow a skill has to be, and the scope tends to vary quite a bit. The final bit of (unintuitive) magic here is that skills do not stack beyond 2. This makes it so that even though a character can gain benefits from a multitude of areas it's never too much to keep track of and it always plays very light.

I've also been working on a game myself which is entirely based around skills where skills are very broad and open similarily to the way numenera handles things. In my system I also use d6s, and skills can vary in terms of breadth of focus (e.g. my list of suggested skills at the moment contains both trader and bartering since the choice between the two says something about the character). There is no restriction on what can constitute a skill save that it must be something that a character can apply itself to and something it can learn through practice or study. Mechanically I give players a one point bonus to their die rolls per skillpoint invested in a skill when they attempt something related to that skill, and this simply has a to beat a set difficulty number. The reason I think this works very well in my system is that a character's skills do not only serve to describe what it can do, but is also shows where the character has been in life. This system let's players define their characters through past professions or hard lessons learned in the past and encode those in a simple mechanichal bonus.

More specifically about your suggestions I think there's a lot of room to add incentives for player to be creative with the way they approach a task. Why not allow players to get a +1 bonus if they think of a clever way to do a problem rather than an obvious one? I think this would be a simple way to get players to feel that the way they are playing the game has a strong impact on their success, rather than their fate being primarily determined by rolling lots dice in succession.

I most definitely think there's a valuable design space surrounding open ended skills and d6 task resolution, but it does tend take the game in a direction where rolling the dice is less important and creative play becomes more key. In the end it's all about what type of experience you want to generate with your game, and that's all up to you. I'd say keep fiddling around with your systems though, you never know what tiny little change will be just what you need when you're working with small numbers.