@TheGander The shame you're feeling's imposed by society, often on people already suffering from what's beyond their control. It won't help. Try and dump it with the fridges contents if you can.🙂
Have cleaned out and salvaged some truly severe fridges sometimes un-refrigerated, left full of rotting food. As you've found, that one's salvageable.
IME the seals won't be helping, but the smell's potentially coming from fridge drainage system, and/or has been absorbed by the plastic body.
It could be something else, but an off cheese smell (nauseating clinging rancid cheese/old feet combo) is potentially caused by fungal spores. (similarly found in wardrobes, bedding, laundry piles, shoes, if uncared for feet - foot/toenail fungus/athletes foot present, or long term dead animals animals and moisture combined.) The instinctive gack response is telling you not to breathe it.
I'd suggest 'professional level' cleaning to ensure future food safety as well as no smell. You're clearly someone able to DIY this too, you've done the worst bit.
The fungicidal disinfectant I'd use will safely kill fungal spores including within a fridges drainage system; Sodium Tetraborate Decahydrate. (old school Borax) Disinfects & kills fungal growth rather than reducing it to less detectable levels.
(It's a strong alkaline powder. Nowadays sensible to treat as noxious when using. Face mask, rubber gloves, don't ingest or breathe in as powder. Ensure entirely cleaned from fridge/surfaces afterwards.
Relatively recently been discovered to have nasty side effects if ingested or repeatedly overused which it has been for decades, and still is in the US including in toothpaste. But it's safe enough if used sensibly, as one off restoration, or continuously in a controlled way in various trades.
You can no longer buy it in UK, but it's not illegal to buy and import. I still use it both for dealing with sewage flooding, and within my work.)
You need to look at the drainage system. You are looking for what can only be described as a 'mucous plug' of jelly like gunge around or in the drainage filter. It can easily masquerade as just a dark drainage hole, but when hooked out is a small dark centered 'jelly' with up to inches of trailing 'fronds.'
You may not find one, but there often is, blocking the drainage of the fridge.
To sort: removed any visible gunk, mix a strong but still liquid solution, trickle a small amount into the drainage system & leave. It will work it's way through.
Thoroughly wipe all surfaces with solution, leave for a few hours. Same with all detachable parts. Wash off with hot soapy water. Dry. Personally I'd then give it a go over with Detox or similar, but that's more reassurance than need. Any residual trace of smell can be dealt with by open pot of bicarb or charcoal.