Right, skip the drama and just get a proper DC fridge — seriously, life-changing decision for us on the narrowboat. A 12V or 24V Waeco or Fogstar unit pulls maybe 40-50A running current, zero inrush nonsense, and your battery bank actually likes you.
If you're wedded to mains fridges (fair enough, they're cheaper upfront), then yeah, you need at least 4-5kW inverter to handle the startup spike — @DriftWizard's right about that being teeth-rattlingly brutal. But that's suddenly a massive battery bank investment, plus the standby losses are mental.
The real question: are you running the hut 24/7 or seasonal? If it's weekend use, a DC fridge barely dents your Victron system. If it's permanent, suddenly a 3kW Pure Sine and a beefy battery setup starts looking reasonable, but you'll want to invest in a soft-start or one of those clever relay modules to manage the inrush.
What's your current battery capacity looking like?