If you're at all handy - or know someone who is - you can build / re-build stuff with a combination of Spectra and Epoxy.
Spectra is a (stronger-than-steel) fibre that is easily bought at a Burnsco / marine chandler.
It comes in the form of rope - sold by the metre - in diameters from 2mm up to large diameter rope.
Great stuff for sailing, camping - just as zero-stretch rope.
The magic comes when you saturate it with epoxy and let it cure - formed into a shape you want.
You get super strength locked into a very strong matrix.... a bit like reinforced concrete, but way stronger and lighter.
I've used this trick in boatbuilding and in repairing lots of difficult shapes: split tentpoles, a cast-iron bandsaw frame, putting a key-ring loop on a USB stick.
It's lightweight, strong as, doesn't rust, fatigue or degrade.
So, for a fridge shelf, you could shape some thin 2mm or 3mm spectra to match the broken-off load-bearing bits and then extend the spectra like a spider web onto the shelf. Saturate with a nice 'runny' epoxy resin (not fiberglass resin) and let it cure. You'll be able to swing from it ;-)
Make sure to buy a nice yellow, red, green - whatever - spectra, to match your fridge decor ;-)
If you're going to 'mould' it in-situ (in the door of the fridge) remember to put a generous layer of olive oil (or a thin layer of petroleum jelly) anywhere you will want to be able to separate the strengthened/repaired shelf from the fridge door. Epoxy doesn't stick well to grease !
For anyone thinking this might be useful in another 'job'... there's one limitation.
Don't use epoxy if it'll get really hot.
Some boat-building epoxies soften up above 50 or 60 C.
That's risky even for a black-painted hull in NZ sunshine.
I know there are epoxies used by the aircraft guys that go way up in temp - but I've never had to use them.
JayADee::( despite that, two places i'd try are leader n watt and B&M electrical here in palmy.MadEngineer:
Thanks but tried them, they don't have any of the fridge side ones. LG confirms there are none...