Just a thought.

[microprediction]

What if you mapped the simplex into the cube (e.g. https://math.stackexchange.com/questions/384713/looking-for-a-nonlinear-map-from-n-dimensional-cube-to-an-n-dimensional-si)

Then you could support rectangular domains easily. Is this something you've considered?

Incidentally, you may be aware of https://stefan-endres.github.io/shgo/ and if not you may be well placed to appreciate it.