I am producing a publication-quality plot to be embedded in latex and I would like to be very precise in terms of sizes and fonts (so that fonts are of the same size in the
The problem you are having is that bbox_inches='tight'
just removes all of the extra white space around your figure, it does not actually re-arrange anything in your figure, after it has been rendered.
You might need to tweak the parameters you pass to tight_layout
(tutorial) to get your desired effect.
Hopefully this gets you pointed in the right direction.