I have specialized somewhat in being a generalist intellectual. I know of two key strategies for pursuing this. The first one is pretty obvious, but still important: learn the basics of many different fields. The more fields you know, the more chances you will find to apply an insight in one field into another. So not only learn many fields, but keep looking for connections between them. That is, keep searching for ways to apply the insights in all the fields you know to all the other fields you know.
Your approach reminds me of a discussion about BreadthFirstLearning I read on c2. Rigorous (or fearful as you call it) checking seems reasonable for a researcher "intruding" into other's fields. I also like to look into many fields and draw connections but my "strategy" was quite the opposite: Push each presumed connection to the extreme and see what happens when discussing it. I didn't do this as a conscious strategy must mostly out of curiosity combined with overconfidence. The upside is that it leads to very quick responses that uncover flaws but also key insights (Cunningham's Law). I could afford it as a youth and student and in a circle of friends. But it wouldn't have work for a professional academic.
By checks, do you mean quick questions like 'does this proposal conserve energy', 'would this imply there's loads of money left on the table that's easily accesible' etc? If they are as easy to apply as the former examples, then it would be great if you could write down your tests in one place. I would find those very high value.
Also, when you talk about connecting ideas, do you usually start by exploring new ideas in the context of some old problem which you have already chunked? Like if you just learnt about symmetry group representation theory, maybe explore the ideas in terms of the lattice structures and their observables if you're a solid state guy.
There is some analogue here with portfolio managers looking for ideas across different fields and asset classes. The critical audience is the market.