I adore the mork borg system, but similarly have been limited to one shots as well. But one thing that stood out was that just a bit more hp dramatically improved their staying power.
Characters closer to ~10hp could survive a whole session. So my thought was to run a DCC style funnel with MB characters and have the selected survivors get better right after. They should hit that ~10hp staying power while still being squishy.
I love my Pirate Borg. It's certainly not as in your face like Mörk Borg or Cy_Borg, but it's far more approachable. I would highly recommend it as a starter Borg. Easy to read and an easy atmosphere to drop into.