Adam Lindsay wrote
Any suggestions [of possible fonts that mix well with euler] beyond my beloved Charter?
I've had a look at your pdf, chironeu.pdf, and was startled at how informal it looks compared to when it's typeset with mathtimes.
In LaTeX, I've seen Euler mixed with Palatino (in the package mathpazo), where Palatino is typeset with an extra 5% leading. I've also seen it typeset with Pandora. I liked the way it mixed with Pandora.