It may be impossible to always get the conceptual stage right first time, but one can adopt a policy of getting it as firm as possible...rather than a policy of cpnnitatiinally associating conceptual analysis with "semantics", "true essences" and other bad things, and going straight to maths.

I think you've got this backward. Conceptual understanding comes from formal understanding--not the other way around. First, you lay out the math in rigorous fashion with no errors. Then you do things with the math--very carefully. Only then do you get to have a good conceptual understanding of the problem. That's just the way these things work; try finding a good theory of truth dating from before we had mathematical logic. Trying for conceptual understanding before actually formalizing the problem is likely to be as ineffectual as going around in the eighteenth century talking about "phlogiston" without knowing the chemical processes behind combustion.