Thank you Yordan! That didn’t necessarily help directly, however it led me to learning about the Appearance property. Best I could find is something like:
select {
-moz-appearance:none; /* Firefox */
-webkit-appearance:none; /* Safari and Chrome */
appearance:none;
}
This will at least remove the system-generated arrow (or wherever it’s coming from) so I can then add my own. Thanks for the help!