I would bedline it with Bedliner that matches the paint after cleaning out the rust. You can see that the rust settled into the low areas that would get wet and the water would sit in those areas causing rust, under your soaked carpet. I had my entire bed and walls cleaned and coated with a nice white bedliner to match my exterior. It is a common practice in Jeeps. This is where I got the idea, right here on this forum. There are many forum threads about it. No carpet means no soggy, settling water. If my interior gets wet, I easily dry it. Plus, I believe it is great sound dampening. I have no carpet and most of the time, I don't even play music, because my Jeep is so quiet. I did put down floor mats and that helps with sound dampening too. I plugged them in place, high under my dash, so they don't move. Plus, any water without the carpeting is easy to see and dry up. There are many different types of Bedliner too. There is Raptor Liner, Monsta Liner, Line-X, etc. I even found one Jeep done in Blue Bedliner.
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