I think you mixed up the order of step 2. The piece of fat should be at the end to lubricate the cooking service. Wetting it again after would be counter productive.

Also I don’t recommend a regular sponge for the water cleansing step due to the materials involved not necessarily be heat safe. Soaked paper towels work great.

I would not use paper towels on the same basis you choose not to use a sponge.

It’s likely not ideal but I rather breathe and possibly consume trace amounts of burned paper than burned sponge.

EDIT: ... and immediately after writing this I googled “paper towel carcinogens” and ruined my day.

Sorry to be the bearer of bad news.

The problem is some propane grills are fairly low power and will require a long time to "burn off" the grease and other stuff. I routinely do it with mine, but it takes at least 10 minutes full blast...

If your grill is dirty enough, you may end up causing a fire that will burn through the enclosure (I've seen it happen). It's also fairly polluting, so if anyone's outside it's best to clean some other way. I like the onion trick myself.

half of a potato works well too.

coca cola works great to clean