So this is the text of the email I got from Weber's customer service, including all the tips they have for cleaning the grill plates:
Thank you for your enquiry and photos. I’m sorry your grills have rusted over time.
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Your original grills are still covered by our five year warranty, and so I have organised for you to receive replacements. The new grills are made of semi-gloss enamel, which means they are less prone to rust.
I have arranged a replacement set of grills to be couriered out to you, and a signature is required on delivery. You will receive an email so you can track your parcel. Your order reference number is PS 661181
A lot of things can contribute to rust, it is important to keep your weber out of the elements, so particularly if you live near the sea or have a pool, Salt from the ocean and chlorine in the air can contribute to fast rusting.
Avoid leaving your grill wet at any time, including after cleaning (never use cold water on a hot grill, this causes hairline fractures in the enamel it will then crack, flake and start to rust.
For day to day cleaning of the grill, the best method is to use a Weber grill brush.
After pre-heating your barbecue, while the grill is very hot, brush along the grill bars where food residue remains, alternatively you can clean your grill this way while it is still on after cooking (don't use any water on a hot grill).
It’s not necessary to wash your Q grill in water after every use but the grill should be washed in hot water and detergent after every five or six cooks to remove excess grease.
It’s handy to re-oil the grills from time to time. Simply remove from the BBQ and pop some oil on; spray oils can be good for this. When you place them back in the BBQ simply heat up the BBQ on low for 5-10 mins to re-seal the grills. (If you use your trivet a lot, for roasts or pizzas etc this can prove beneficial).
Try to keep the grill protected from the elements, particularly if you live near the sea or have a pool. Salt from the ocean and chlorine in the air can contribute to corrosion.
I've always just used the Weber grill brush, never used water on a hot grill. I do often grill stuff like chicken skewers that are marinated though, and the sugary marinade sticks like shit to a blanket. I really don't think that's the flavour I want to keep on it! I think I'll be much gentler with cleaning that type of stuff off this time around.