I checked after u/Rjeezy88's comment, and a regular 2.54mm pitch female header plugs in (though it doesn't locate), so my current solution is this kit:

https://www.amazon.com/gp/product/B07TB8QXMC

I'd still be interested in the 'right' connector that mates properly and prevents being hooked in wrong, and locks in better for vibration resistance, so if anyone has a lead on the 'proper' connector I'm all ears.