Man thats annoying.
This conversation got me interested again, and I found this:
https://www.digikey.com/en/products/detail/te-connectivity-amp-connectors/1658694-2/765668
It is VERY close to working, the height looks good, the base looks good, its got one flaw. The pins for connecting it to the pcb are too thick, and too long. Too long of course can be fixed, but too thick might be a pain. Filing them down might be an option. Or, the search continues.