Great idea for a theme. I just started the Pre-Sequel earlier this week and it's been great getting back into the Borderlands universe.
Obviously this would be a huge scope increase, but any thoughts on having two modes? I hear you on not wanting to have a story mode, and I think that's the right call, but one of the biggest draws to Borderlands for me is getting access to better and better weapons as you level up and get better drops. I feel like cramming that progress into a three ball game could be really tough. I like the idea mentioned above about allowing you to continue progression across multiple games. Dunno if you play any virtual pinball, but Epic Quest by Zen does this very well.
And then a normal/tournament mode that could just be a standard three-ball affair.