[morzh]

I am not a transformer design specialist, so...I would look into how a known good transformer is designed.

Actually, in the pulse transformers, to kill the leakage field, they wrap a turn of foil around the transformer (not around the bobbin, but the whole thing): this will act as a shorted turn, but only for the leakage field.
Of course, this is a different animal.

But as I remember, even low-frequency transformer, if designed for high quality applications, ain't that straightforward.
They use sectioning, and interleaving, to minimize and optimize stray parameters.
There was a good book I saw at my ex-boss' library, by some old expert, an Army colonel, actually. Large book, very detailed.
Many things in it, other than "wind your primary and your secondary"

I also suspect that by making some strategic cuts in metal of the chassis around the transformer, one could possibly localize the eddies.
But this would require lots of experimentation, to prove or disprove any of the theories.
To me, the best way is to try to analyze the existing successful designs.