I was also thinking that you could add extensions to the uprights.
Lets see, the best way to describe it. A short piece of square tubing that fits into the upright, then a piece welded going horizontal (out). Then another short piece welded so that it is sticking up. Your tarp would then attach to this. The only thing to touch the stand would the the tarp suspension at the ends.
Clear as mud?
Then if your using this inside or just for a nap and don't need/want the tarp, you can just leave the extensions off.
That would work, too.
With any stand used outside, it's a good idea to tie it down. Gusty winds will knock a stand with hammock attached over the first time you turn your back.