I play music all day on my Echo and Echo Dot. I got frustrated with hearing the same music repeatedly when I knew I had over 220 songs as "favorites" or "likes". After research, trial, and error I realized Alexa only shuffles about 20 songs at a time. Here's my solution.
I opened the Amazon Music on my laptop, sorted in alphabetical order by song title (this gives you a nice starting shuffle).
I took 20 songs at a time and created 11 playlists: Favorites 1 - 11
I established a speaker group and gave it a custom name: mine is Combined Speakers. One in the living room and one in the bedroom. No matter where I walked in my home I could hear the music.
I added my Echo and Echo Dot to the group.
Here's the important part: playing on the speaker group is pre-determined by saying the phrase "play music". So, I would say "Echo, play and shuffle Favorites 1 music". At first I had to tell Echo at the end of the phrase "on Combined Speakers". But after the first two times it wasn't necessary.
A playlist of 20 songs will play continuously for about 1.5 hours. When it stopped, I would just tell it to play the next one.
Now, I have 220 songs playing and shuffling continuously.