The adapter is rounded down on the outer edge to make putting a record over it easier and tall enough to be easy to grab to remove from the spindle. A taller version with more pronounced outer edge rounding is also included.

In case three points of contact with the record isn't stable enough (or you just like the looks) I added a 4-ring variation.

Customization:

I included the OpenSCAD file that I used to generate the models. All key parameters are defined and commented for use in the customizer. The models I uploaded are included as presets in the customizer and their details can be viewed at the bottom of the file.