Great topic. I recently started a conversion/rebuild, and am wondering the same thing. We are not carpeters. I figured that if you want to wrap the storage lids with carpet, you will have to cut the carpet lager than the storage hole so you can wrap it around the deck, and then use seperate pieces to wrap the lids...? So you are talking about more carpet and more cutting/shapping...
Here's what we are thinking, but I'm not sure how it will look. We are thinking we build the frame; put down the deck; cut the lids; put down the carpet, and then cut the carpet around the lids. Now, you'll have rough edge on the carpet, which looks bad and will tear up, unless we trim it. We are thinking of using trim like you would use on stairs (which is angle iron made of anything from aluminum to rubber). It will be simple to install, and it will cover the rough edge of the carpet. PLEASE...feedback would be great.