I have this one on my 27' round pool.
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I think I got it at INYO pools, but it is the same product. You could go with a smaller one to cross your 16' width.
Now, this cover is meant to bolt to the top rails of the pool, and clearly your Intex is not going to support that.
What you can do is bury a 4x4 post on each side of the pool, maybe 6" or so away from the sides, level with the top of your pool, and attach the end mounts to that.
In fact that is what I did in a separate part of my yard. Since I have a round pool, the cover reel goes right across the middle of my pool. I have two 4x4 posts off to the side of my yard. I roll up the cover, pivot one end of the reel to one post, and then the other end to the other post. I have 8' posts buried about 4' into the ground, and they are just fine. In fact over the winter my cover lives on those posts, wrapped up in a tarp, and trussed up like a giant sausage in my yard.
The sections of aluminum tube are held together by drilling a hole, inserting a rubber plug, and then tightening a bolt into the plug, expanding it. Those lasted about 2 years and then started falling out (it does not cause the reel to fall apart, just allows it to possible expand when you are swinging it). I bought some stainless steel carriage bolts and nylock nuts and used those to replace the rubber plugs. I am still happy with how it has been working.
