I'm making a custom transformer with some e cores and a small air gapMercury vapor ballast use saturable transformers and the secret sauce is in the steel core.
Or more specifically, the width and location of the air gaps.
The steel laminations are not your normal E-I cores. They are very special stampings with a particular steel grade.
The sloppy windings are the least of your worries.
It will be running off of a royer push-pull oscillator.This is a fet gate drive circuit, or a forward transformer, or flyback type transformer or current sense transformer?
If you want good coupling you should space coils evenly across the bobbin.
Also use interleave winding.
Also beware having turns too near a big gap due to fringing field heating.
Avoid too may layers of single core as you get skin effect and proximity loss.
Use litz wire if its high frequency.