Hi @ed727!
Interesting. I have been through many instances where fixing a responsive behaviour takes me hours to fix 
I have not come across what you are describing though.
I decided to create a solo group with a fixed width setting and a text element with a 20% min width on a page with its responsiveness activated.
Please review an extract of the bubble manual guide on this below, as well as, two screenshots of the solo group expanded or contracted.
In both cases fixed width worked and the group did not expand nor contract.
Perhaps, you could review all the nested up and nested down elements of your build and check for all of their responsive settings? … (easier said than done … I know!)