I have the same problem. I broke my middle finger when I was a kid, and can't straighten my finger, so that nail catches. I have to keep my nails very short or get clank from my middle finger.
Hipshot 3/8 are a drop in fit. I have them on a Streamer std.
The Schaller above has the screw hole in the wrong place. They are M4 180, you would need M4 90.
https://schaller.info/en/machine-heads/292/m4-90-light?c=53
Gotoh GB707 should fit. https://g-gotoh.com/product/gb707/?lang=en
Can read but only treble clef. Just can't get my head round bass clef. Was taught treble clef as a kid, and have tried to teach myself bass clef, but just get confused, so use tab and YouTube for bass.
Nordstrand make a 51 pickup in a jazz housing.
https://nordstrandaudio.com/collections/4-string-jazz-bass-pickups/products/51-split-j-1
These in a standard jazz body may give you what you're after.