How random is random?

Running LMS 8.1.1 on MacOS 11.2.3.

I’m toying with a few variations to get combinations of my server library and/or Spotify library playing random (or shuffled, if you prefer that term).

At present I’m using Random Mix. I’ve set its genre checkboxes on the web UI so that it accesses what I want from my own server library of tracks and from my Spotify stuff. This works well.

Sometimes, though, I want to have only my Spotify stuff playing in random/shuffle mode. I’ve tried this with Settings/Shuffle set to Shuffle By Song on the SB3 but have had what we might call less than random results. I mean, much as I like Steely Dan, Blue Nile, and a few others, their tracks do turn up much too frequently to deserve the term random. There are loads of tracks and artists that just never ever turn up.

So, my two linked questions.

1. Is there another way to do random that I’m missing and that might suit my requirements?

2. Is there a way to set up more than one set of prefs for Random Mix? It occurs to me that it would be nice to have an option where just the Spotify checkbox is checked, in addition to the one I’m using. In other words, I could choose between a random feed from Mine+Spotify and a random feed from Spotify-only.