Since there's no standardized way of saving high scores in games, if any at all, I coded a little website to store my high scores.
I've got a cronjobbed script on the MiSTer that reads the active core from a temp file and curls it to my server.
A live mode on the website anchors to the relevant game in (near) realtime, as shown in the video.
High scores and initials are stored in a database, so it requires manual input on the website, but at least it's all in one place.