When I had a sticks and bricks we had issues with the door on the freezer on the residential fridge therein...
Used one of these to fix it.
Refrigerator Travel Locks - Latch Style - RV Designer H593 - Interior Hardware - Camping World
Worked great.. of course this unit was not bouncing down the freeway at 55 mph but still it worked great.. might work for you as well.
Another thought is a variation on the pin lock used on many RV fridges.
on my kitchen drawers here in the motor home the latches are not all that good,, So I got a couple of "Eye" bolts, these are lag bolts (not what you'd use on a fridge) with about a half inch EYE.
I drop a dowel road down through the eyes it is a 4 drawer stack, the eyes are beteen 1&2 and 3&4) and they do not come open till rod is removed. it's the old 2x4 across the door method but you could put loops of some kind on the unit and use a method like mine.
What do I use for my fridge: I do not have a residential fridge here. Just a very nice properly latched Dometic that works flawlessly.. Yes, I could use a bit more room but frankly, not all that much.
Wed is Senior Discount day at the local Supermarket so I do my major shopping every WED
Sunday the same supermarket is on my way to/from Church so I do my fill in shopping on the way home from church.. And I really enjoy going to church and singing in the choir.
NOTE: all the campgrounds I stay at.. There is always a supermarket between church and CG, (Church is always near one it seems).
Usually in the winter coming out of church I have my choice (Wal*mart, Bi-Lo, Aldi, occasionally Food Lion and Ingles depending on the Campground) here in GA it's Bi-Lo and soon Dollar General (Already a DG but they are moving and expanding). Summer depending on the CG Meijer's or Krogers awith Wal*mart and Aldi being only a short drive out of my way. But always good shopping on the way home so I do not need to fill the fridge with 2 weeks worth of food.